When you get your pilot licences first time , your licence and medical have to be on the same authority. Thatswhy you transfered it to Spain . After you issued your licence you can renew medical examination in any state in EU. I think there is nothing to do with French CAA. Your medical issued in Spain now, most probably they will check more than regular renewal examination, It will be close to initial examination and thats it. You will get your medical cert. and you dont have to do anything more . AME or AEMC will send results to Spain CAA. Be sure, you said the AME you have foreign medical cert, because some of AMEs dont do medical check for foreigners medical certs. ( This is how it worked with me, maybe some countries have different rules, better to ask your CAA )