Only two possibilities exist for after France’s capitulation, it will fall, the Morning might come again, but it will fall during G1 or G2.
The first being is the French navy, probably the majority will be the Mediterranean, maybe something in the Atlantic as well. Since the there is no Vichy element, and no ‘bad blood’ between them and the British, there’ll be no loss of lives (and vessels) between allies. I can see the fleet regrouping, but most likely forming multinational defense rings with England and America. Whatever is left of the fleet that is…
As the land forces, ie infantry, they’ll be scattered in Africa and the Middle East (Syria), again, the only worthwhile option is to form multinational defense, to help the Allies stem the tide. I doubt they’ll be making many offensive campaigns.