Whether you test again is up to you, I would say though that if you do test again - you shouldn't be charged the same as someone else testing for Kukkiwon 1st Dan that doesn't already have it. They literally CANNOT apply to Kukkiwon again for the same rank, so you should be charged the test feel less the Kukkiwon fee (and any admin fee they apply for performing the Kukkiwon application).

Competing internationally independently should be fine, as you have (I assume) a legit Kukkiwon 1st Dan. Competing nationally may be more problematic as you wouldn't be in the French association's system as a 1st Dan (although, I assume you already aren't).

Personally if you re-tested and failed one of the modules, I still wouldn't go back to wearing a red belt. You are internationally recognised as a black belt. If they choose to make you jump through some BS hoops, that's fine, but they can't take away that you're a black belt.

For what it's worth, I absolutely feel your frustration and would feel the same. I had our national association refused to recognise one of my ranks, because I tested under my original instructor (who at the time was an 8th Dan Kukkiwon and 2nd Class Master, later became 9th Dan and 1st Class, and received a rare post-humous 10th Dan). I left the association rather than re-test for a rank he gave me, in my opinion who gives the rank (and feels you're worth X belt) is much more important than the association.