the feds will recognise your IR as well with just a written test.
Indeed.
However, the FAA does this only for piggyback (61.75) FAA PPLs. If you have a standalone FAA PPL or CPL then the foreign pilot IR route is not available (I am told).
That French validation for non EU residents only is such a crude trade protection scam... only the French could do something so "in your face" and get away with it. In the UK, they at least follow the Yes Minister guidelines to put at least a proper veneer of respectability on things