Yes you can - correct - but you cannot use a FAA IR in a G reg aircraft which is pretty much the only reason why anybody gets a FAA cert - in conjunction with a N reg aircraft in Europe.
Simply using a FAA cert in a non N reg aircraft in Europe really achieves nothing. In fact you cannot use a FAA cert in France to fly a F reg - if you are a EU resident.
I know, but I use my FAA PPL Rotorcraft to fly G-Reg in VFR, which DGAC also allow me to do in France.
I have no intention to fly choppers IFR...I do have fixed wing IR MEL/SEL on FAA also and fly N-reg aircraft..so see that would pose an issue if the IR were not allowed.