No, not strictly true.
If you want/need another member states licence, firstly, you will need to transfer your medical records from the CAA (at cost) to the French (DGAC?)
The CAA will take their time on this. It took me two months to get the CAA to do this. (This wasn't to the French)
French licence = French medical
British licence = British medical etc.
You will loose any national ratings previously held, if any. Also, they won't transfer any expired type ratings to the new licence.
CAA +44 1293 573700 ask for medical department. They will take a card payment over the phone for the transfer. You will also have to scan a letter with signature giving them express permission to release your medical records.