The front and rear derailleurs operate completely independently from each other - one has no impact on the other - just to get it out of the way. In the front, it should be possible to make any shifter to work with any derailleur. This is because you tune the derailleur extension for the middle ring by tensioning the shifter cable and the extensions for the inner and outer rings are regulated with the stop screws on the derailleur. The outer ring rating of the derailleurs has some but not critical impact on operations - you can get the derailleur working no matter what that ring is. (Size difference between middle and outer may matter, if it too small, but then the derailleur gets blocked which does not seem to be the case here.) Excellent instructions for novice front derailleur adjustments are provided on the Park Tool site.