Silly thought... can you get the examiner to hang on to the paperwork? When you receive your French licence, go back to the examiner, send in the paperwork for the flight you already did and have that processed by the DGAC. If the examiner who flew with you is not AESA registered, he was allowed to perform that skill test for a French licence holder, so just await the licence and take it from there. The main downside of this is of course that you cannot exercise the priviliges of that licence while you await your new papers... but it might be a way out.