Some good ideas here. This got me to thinking… if someone really wanted to play France as a country, buy units, etc.; then you could play it this way:
French player starts out with the Allies, but once Germany takes the capital, they play with the Axis. The capital and all territories remain in French hands and they still retain their income and build on their factories. When/if the Allies liberate Paris, the French player then joins the Allies. Each time Paris in taken, any French units in territories occupied by other nations remain Allied and usable by that nation (like the French fighter and soldiers in England and boats in the same territory as the British). If the Allies take Paris, any French units with German/Italian/Japanese combat units in Russia/Germany/the water/wherever are usable by that nation. The rules are mirrored for if the Allies take Paris: France retains control of their income and all their territories that they control and simply fights with the Allies.
Aspects of this would actually be similar to how it was in the war. Although you didn’t have stacks of French soldiers defending Normandy from Allied invasion (though some French soldiers fought for the Axis), you also didn’t have the French Mediterranean fleet, Morocco, and southern France fighting against the Axis after France capitulated.
I’m not sure if this might even be balanced or whether it might swing to Allies or Axis. The push towards Russia would be hampered as some units would need to come all the way from France and those units would attack out of turn from Germany, but on the other hand the Axis would have more total income and a D-Day invasion would be much harder.
We always play with all the Axis playing at once and all the Allies playing at once, so that would likely give the Axis an advantage, but you could compensate by giving the Allies more money.
As an optional rule, you could allow the Japanese player to conquer French Indo-China (just as in the war and just to spice things up) or leave for the French player (maybe France could build a factory there?). This decision could be strategic by the Japanese player: allowing money to flow where it’s most needed, or it could be cordial: gentlemanly to leave it to your new co-belligerant, or it could be playfully poking fun: haha, it’s mine and you can’t do anything about it. It might make the Japanese player less ‘lonely’ to have some interaction with their co-belligerants.
The French player might have some disconnection with who wins (or might slightly favor Axis since that’s where their reputation as a skilled player is on the line), but on the other hand, it might be a happy ending to be on the winning side no matter which side won the game. Another plus is that for a Europe only game, the sides would be an even 3 on 3 for the nations for most of the game and it might allow you to have a 6th player on the Europe only board.