There are probably several problems here.  (And I remember having added those cycle routes a few years ago after a couple of surveys, a lot of guessing and not the convenience of the 360° photo coverage we are having now.)

https://www.mapillary.com/app/?pKey=1389393742509793 → the ICC sign sends cyclists to the left, and I suppose it means crossing the boulevard to use https://www.openstreetmap.org/way/144270575.  That solves the problem if small Lambermont alley which is one-way + the one-way cycle connector which the relation currently uses in both directions.

After that, the cycle relation can use this connector https://www.openstreetmap.org/way/1131443679 and take the cycle lane on the boulevard, and it should work.