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<P STYLE="font: 10pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt; text-align: center"><B>UNITED STATES<BR>
SECURITIES AND EXCHANGE COMMISSION<BR>
Washington, D.C. 20549</B></P>

<P STYLE="font: 14pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt; text-align: center"><B>FORM 8-K</B></P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt; text-align: center"><B>CURRENT REPORT<BR>
Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934</B></P>

<P STYLE="font: 10pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt">&nbsp;</P>

<TABLE CELLSPACING="0" CELLPADDING="0" STYLE="width: 100%; border-collapse: collapse">
<TR STYLE="vertical-align: top">
    <TD STYLE="font: 12pt/106% Times New Roman, Times, Serif">Date of report (Date of earliest event reported)</FONT></TD>
    <TD STYLE="text-align: left; border-bottom: Black 1pt solid; font: 12pt/106% Times New Roman, Times, Serif; padding-right: 5.4pt; padding-left: 5.4pt; vertical-align: bottom; width: 60%">June 16, 2020</TD>
    </TR>
</TABLE>
<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 16pt; text-align: center">&nbsp;</P>

<TABLE CELLSPACING="0" CELLPADDING="0" STYLE="width: 100%; border-collapse: collapse">
<TR STYLE="vertical-align: top">
    <TD STYLE="border-bottom: Black 1pt solid; width: 100%; font: 12pt/106% Times New Roman, Times, Serif; padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">First
    Trust Enhanced Equity Income Fund</TD></TR>
<TR STYLE="vertical-align: top">
    <TD STYLE="font: 12pt/106% Times New Roman, Times, Serif; padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">(Exact Name of Registrant as Specified in its Charter)</TD></TR>
</TABLE>
<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 16pt; text-align: center">&nbsp;</P>

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<TR STYLE="vertical-align: top">
    <TD STYLE="width: 34%; border-bottom: Black 1pt solid; padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">Massachusetts</TD>
    <TD STYLE="width: 33%; border-bottom: Black 1pt solid; padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">811-21586</TD>
    <TD STYLE="width: 33%; border-bottom: Black 1pt solid; padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">30-0261406</TD></TR>
<TR STYLE="vertical-align: top">
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">(State or Other Jurisdiction of Incorporation)</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">(Commission File Number)</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">(IRS Employer Identification No.)</TD></TR>
</TABLE>
<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 16pt">&nbsp;</P>

<TABLE CELLSPACING="0" CELLPADDING="0" STYLE="width: 100%; border-collapse: collapse">
<TR STYLE="vertical-align: top">
    <TD STYLE="width: 50%; border-bottom: Black 1pt solid; padding-right: 5.4pt; padding-left: 5.4pt">
        <P STYLE="font: 12pt Times New Roman, Times, Serif; margin: 0; text-align: center">120 East Liberty Drive, Suite 400</P>
        <P STYLE="font: 12pt Times New Roman, Times, Serif; margin: 0; text-align: center">Wheaton, Illinois</P></TD>
    <TD STYLE="width: 50%; border-bottom: Black 1pt solid; padding-right: 5.4pt; padding-left: 5.4pt">
        <P STYLE="font: 12pt Times New Roman, Times, Serif; margin: 0; text-align: center">&nbsp;</P>
        <P STYLE="font: 12pt Times New Roman, Times, Serif; margin: 0; text-align: center">60187</P></TD></TR>
<TR STYLE="vertical-align: top">
    <TD STYLE="font: 12pt/106% Times New Roman, Times, Serif; padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">(Address of Principal Executive Offices)</TD>
    <TD STYLE="font: 12pt/106% Times New Roman, Times, Serif; padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">(Zip Code)</TD></TR>
</TABLE>
<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 16pt">&nbsp;</P>

<TABLE CELLSPACING="0" CELLPADDING="0" STYLE="width: 100%; border-collapse: collapse">
<TR STYLE="vertical-align: top">
    <TD STYLE="font: 12pt/106% Times New Roman, Times, Serif">Registrant's telephone number, including area code</TD>
    <TD STYLE="text-align: left; border-bottom: Black 1pt solid; font: 12pt/106% Times New Roman, Times, Serif; width: 70%; padding-right: 5.4pt; padding-left: 5.4pt; vertical-align: bottom">(630) 765-8000</TD></TR>
</TABLE>
<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 16pt; text-align: center">&nbsp;</P>

<TABLE CELLSPACING="0" CELLPADDING="0" STYLE="width: 100%; border-collapse: collapse">
<TR STYLE="vertical-align: top">
    <TD STYLE="font: 12pt/106% Times New Roman, Times, Serif; width: 100%; padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">&nbsp;</TD></TR>
<TR STYLE="vertical-align: top">
    <TD STYLE="border-top: Black 1pt solid; font: 12pt/106% Times New Roman, Times, Serif; padding-right: 5.4pt; padding-left: 5.4pt; text-align: center">(Former Name or Former Address, if Changed Since Last Report.)</TD></TR>
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<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 16pt">&nbsp;</P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt">Check the appropriate box below if the Form 8-K filing
is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions (see General
Instruction A.2. below):</P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt">[&nbsp;&nbsp;&nbsp;] Written communications pursuant to Rule 425
under the Securities Act (17 CFR 230.425)</P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt">[&nbsp;&nbsp;&nbsp;] Soliciting material pursuant to Rule 14a-12 under
the Exchange Act (17 CFR 240.14a-12)</P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt">[&nbsp;&nbsp;&nbsp;] Pre-commencement communications pursuant to Rule
14d-2(b) under the Exchange Act (17 CFR 240.14d-2(b))</P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt">[&nbsp;&nbsp;&nbsp;] Pre-commencement communications pursuant to Rule
13e-4(c) under the Exchange Act (17 CFR 240.13e-4(c))</P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 16pt">&nbsp;</P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt"><B>Item 7.01 Regulation FD Disclosure.</B></P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt">First Trust Enhanced Equity Income Fund (the "Fund") is filing herewith a press
release issued on June 17, 2020, as Exhibit 99.1. The press release was issued by First Trust Advisors L.P. to report that Chartwell Investment
Partners, LLC, the Fund's investment sub-advisor, will release an update on the market and the Fund on June 19, 2020. Details regarding the access
to the update are contained in the press release included herein.</P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 16pt"><B>Item 9.01 Financial Statements and Exhibits.</B></P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt">(d) Exhibits</P>

<TABLE CELLSPACING="0" CELLPADDING="0" STYLE="font: 12pt/106% Times New Roman, Times, Serif; width: 100%; border-collapse: collapse">
<TR STYLE="vertical-align: top">
    <TD STYLE="width: 4%; padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD>
    <TD STYLE="width: 12%; padding-right: 5.4pt; padding-left: 5.4pt">Exhibit</TD>
    <TD STYLE="width: 84%; padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD></TR>
<TR STYLE="vertical-align: top">
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">Number</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">Description</TD></TR>
<TR STYLE="vertical-align: top">
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD></TR>
<TR STYLE="vertical-align: top">
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">99.1</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt"><A HREF="pressrelease.htm"><FONT STYLE="color: blue">Press release of First Trust Advisors L.P. dated June 17, 2020</FONT></A>.</TD></TR>
</TABLE>
<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 16pt">&nbsp;</P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 16pt">&nbsp;</P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt; text-align: center"><B>SIGNATURES</B></P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt">Pursuant to the requirements of the Securities Exchange
Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.</P>

<TABLE CELLSPACING="0" CELLPADDING="0" STYLE="font: 12pt/106% Times New Roman, Times, Serif; width: 100%; border-collapse: collapse">
<TR>
    <TD STYLE="vertical-align: bottom; width: 7%">&nbsp;</TD>
    <TD STYLE="vertical-align: bottom; width: 41%">&nbsp;</TD>
    <TD STYLE="vertical-align: top; width: 2%">&nbsp;</TD>
    <TD STYLE="vertical-align: top; width: 50%">FIRST TRUST ENHANCED EQUITY INCOME FUND</TD></TR>
<TR STYLE="vertical-align: top">
    <TD>&nbsp;</TD>
    <TD>&nbsp;</TD>
    <TD>&nbsp;</TD>
    <TD>&nbsp;</TD></TR>
<TR>
    <TD STYLE="vertical-align: bottom">Date</TD>
    <TD STYLE="vertical-align: bottom; border-bottom: Black 1pt solid">June 17, 2020</TD>
    <TD STYLE="vertical-align: top">&nbsp;</TD>
    <TD STYLE="vertical-align: top; border-bottom: black 1pt solid">/s/ W. Scott Jardine</TD></TR>
<TR STYLE="vertical-align: top">
    <TD>&nbsp;</TD>
    <TD>&nbsp;</TD>
    <TD>&nbsp;</TD>
    <TD>Name: W. Scott Jardine</TD></TR>
<TR STYLE="vertical-align: top">
    <TD>&nbsp;</TD>
    <TD>&nbsp;</TD>
    <TD>&nbsp;</TD>
    <TD>Title: Secretary</TD></TR>
</TABLE>

<P STYLE="font: 10pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt">&nbsp;&nbsp;</P>

<P STYLE="font: 10pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt">&nbsp;</P>

<P STYLE="font: 12pt/106% Times New Roman, Times, Serif; margin: 0 0 8pt; text-align: center"><B>EXHIBIT INDEX</B></P>

<TABLE CELLSPACING="0" CELLPADDING="0" STYLE="font: 12pt/106% Times New Roman, Times, Serif; width: 100%; border-collapse: collapse">
<TR STYLE="vertical-align: top">
    <TD STYLE="width: 4%; padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD>
    <TD STYLE="width: 12%; padding-right: 5.4pt; padding-left: 5.4pt">Exhibit</TD>
    <TD STYLE="width: 84%; padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD></TR>
<TR STYLE="vertical-align: top">
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">Number</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">Description</TD></TR>
<TR STYLE="vertical-align: top">
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD></TR>
<TR STYLE="vertical-align: top">
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">&nbsp;</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt">99.1</TD>
    <TD STYLE="padding-right: 5.4pt; padding-left: 5.4pt"><A HREF="pressrelease.htm"><FONT STYLE="color: blue">Press release of First Trust Advisors L.P. dated June 17, 2020</FONT></A>.</TD></TR>
</TABLE>
<P STYLE="font: 10pt/107% Times New Roman, Times, Serif; margin: 0 0 8pt">&nbsp;</P>

</BODY>
</HTML>
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{"company-data": {"conformed-name": "FIRST TRUST ENHANCED EQUITY INCOME FUND", "cik": "0001291334", "irs-number": "300261406", "fiscal-year-end": "1231"}, "filing-values": {"form-type": "8-K", "act": "34", "file-number": "811-21586", "film-number": "20970206"}, "business-address": {"street1": "C/O FIRST TRUST PORTFOLIOS L.P.", "street2": "120 EAST LIBERTY DRIVE, SUITE 400", "city": "WHEATON", "state": "IL", "zip": "60187", "phone": "630-765-8000"}, "mail-address": {"street1": "C/O FIRST TRUST PORTFOLIOS L.P.", "street2": "120 EAST LIBERTY DRIVE, SUITE 400", "city": "WHEATON", "state": "IL", "zip": "60187"}, "former-company": [{"former-conformed-name": "First Trust/Fiduciary Asset Management Covered Call Fund", "date-changed": "20040526"}, {"former-conformed-name": "First Trust/Fiduciary Asset Management Covered Call Income Fund", "date-changed": "20040521"}]}
UNITED STATES
SECURITIES AND EXCHANGE COMMISSION
Washington, D.C. 20549
FORM 8-K
CURRENT REPORT
Pursuant to Section 13 or 15(d) of the Securities Exchange Act of 1934
Date of report (Date of earliest event reported)
June 16, 2020
First
    Trust Enhanced Equity Income Fund
(Exact Name of Registrant as Specified in its Charter)
Massachusetts
811-21586
30-0261406
(State or Other Jurisdiction of Incorporation)
(Commission File Number)
(IRS Employer Identification No.)
120 East Liberty Drive, Suite 400
Wheaton, Illinois
60187
(Address of Principal Executive Offices)
(Zip Code)
Registrant's telephone number, including area code
(630) 765-8000
(Former Name or Former Address, if Changed Since Last Report.)
Check the appropriate box below if the Form 8-K filing
is intended to simultaneously satisfy the filing obligation of the registrant under any of the following provisions (see General
Instruction A.2. below):
[   ] Written communications pursuant to Rule 425
under the Securities Act (17 CFR 230.425)
[   ] Soliciting material pursuant to Rule 14a-12 under
the Exchange Act (17 CFR 240.14a-12)
[   ] Pre-commencement communications pursuant to Rule
14d-2(b) under the Exchange Act (17 CFR 240.14d-2(b))
[   ] Pre-commencement communications pursuant to Rule
13e-4(c) under the Exchange Act (17 CFR 240.13e-4(c))
Item 7.01 Regulation FD Disclosure.
First Trust Enhanced Equity Income Fund (the "Fund") is filing herewith a press
release issued on June 17, 2020, as Exhibit 99.1. The press release was issued by First Trust Advisors L.P. to report that Chartwell Investment
Partners, LLC, the Fund's investment sub-advisor, will release an update on the market and the Fund on June 19, 2020. Details regarding the access
to the update are contained in the press release included herein.
Item 9.01 Financial Statements and Exhibits.
(d) Exhibits
Exhibit
Number
Description
99.1
Press release of First Trust Advisors L.P. dated June 17, 2020
.
SIGNATURES
Pursuant to the requirements of the Securities Exchange
Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned hereunto duly authorized.
FIRST TRUST ENHANCED EQUITY INCOME FUND
Date
June 17, 2020
/s/ W. Scott Jardine
Name: W. Scott Jardine
Title: Secretary
EXHIBIT INDEX
Exhibit
Number
Description
99.1
Press release of First Trust Advisors L.P. dated June 17, 2020
.