Dadou
I have a UK issue JAR licence but have my medical with a French AME (in Normandie). The CAA will recognise this French issued medical (of course we are in JAR land now) but only for the first of the two years of issue.
So find yourself a nice French AME locally to do a JAR medical examination and send your paperwork through to the CAA. Will be much cheaper, even if you have to do it each year in France.