The French have a unique lot in any WWII game. Damage control. They will almost always fall, and thus their job is twofold- maximize German casualties, and strike back afterwards. In v3, which the new rules for Vichy, a 3rd is added, defend the empire aginst the Vichy.
The prevailing philosophy among most players is that some form of backup is need. Whether that be a small force in Algeria or Cameroon, or support for Abyssinia, there is almost always a cache of units that attempt to roll Free French so the French have an army.
The inherent problem with that is twofold. One, you are gambling. You are hoping that you roll and get those units on the Vichy rolls. This is a 50% chance, so mathematical half of those units will go Vichy and fight you. That isn’t that great. Even if Abyssinia is used, you still have to win the war, which is hard. Another problem is that you are draining resources from France itself, thus reducing the German casualties. No matter what, it seems something is sacrificed.
But is it? What if you do the unthinkable- empty everything into France. In that case, all forces you own, all you build, and even a militia upgrade for the one in Syria., goes to France. This means that nothing is left in the colonies. I’m not going to talk about where these go inside France, but I will assume you position them ideally. I think that is the ideal French plan. By its very nature it maximes German casualties. Secondly, due to leaving nothing for the Vichy to get, there is no danger of a early breakout in Africa. The only danger from Vichy is in the form of a transport. Hopefully you will have ships to stop that. Finally, you say, there is no French to use now! How will we strike back? By using your greatest advantage. Production. The Vichy cannot build anything, and only receive one lend lease per turn. They get a recruitmentroll, but it is at 2, and that mean you can expect an infantry once every 6 turns, or about 2 per game. Meanwhile, Free France can build, as well as receive at least 2 items of lend-lease, 3 if the Soviets are nice. This allows you to quickly build up a force and attack the undefend areas of Vichy. This then gives more money and allows a faster conquest.
In short, I believe that emptying the colonies and going all out in defense of France is the best tactic for France to empoy. It limits the Vichy options at no risk, maximies German casualties, and still allows for a quick buildup and counterstrike using lend-lease.