I feel your pain. It took me nearly two years of intermittent work
and expense to get a German registered Anschau trailer onto
French registration and that was without any documentary
glitches. I would not have succeeded without the help of a multi-
lingual German lawyer friend: the key was to obtain a German
registration document translated into French - by an official
certified translator (of course). This together with various Anschau
documents and German TuV documents eventually produced a
French registration document just two days before the French put
the whole system "on-line".

The Germans and French have a common land border and have
only been in the EU for about forty years so it's early days to
expect any useful "harmonisation".

Good luck, you'll need it.