All right chaps, here's a frenchman p.o.w on the post defeat France fate.
Having some german HoS and country name is IMHO wrong.
First of all, apart from some minor annexations, Germany wouldn't try to germanize France. Too big, too proud, too old and deep rooted. Hell, in otl they failed to make Alsace a proper part of Germany, and they are a germanic people speaking a german dialect. So it's just impossible with "proper" france. Then, what's the point of any german name, if not for germanization, and even more for any strange name referring to Charlemagne's Empire?
France is defeated and should be keep checked: actually the current mod solution is quite good. Giving northern provinces to Belgium and supporting the creation of regional states where there are strong regional identities.
IMHO, the only thing to change is to have France becoming a weak parlamentarian republic instead of a german inspired monarchy. Germany doesn't want to have to deal with any unrest or resistance against a german inspired throne. And what's left of French royal are probably in Algier.
So, a more severe 1871 solution is quite obvious: Let the French deal themselves with their politics in certain limits. Like Finland after WW2: sort of independent but checked by Soviet Union and having taboos about angering Soviet Union. Puppeted democratic government is IMHO the best solution.
Regarding National France: I frankly think they shouldn't be a republic, hence their flag, nor a monarchy: who will reign upon rump France?
More like Horthy's Hungary or Franco/Petain's regime: French State. Not a republic, not a monarchy. Something with a sort of regent at his head, waiting for the reconquest to occur and to decide France's regime.
Republic? Republic lead France to defeat and I doubt revanchist exiled nationalists would refer and use the cause of France downfall.
IIRC, new National France events will allow the player to choose a republican way or normalizing the country. It's good it's not the only path, as I believe a sort of regency waiting for the reconquest fits more with National France backstory and ideological fundations.