Keep in mind that the following POD will have very few ramifications on the outcome of WWII, that is not what I'm interested in. I'm more interested in the effects on the political future of France.
Now in OTL the fate of Admiral Francois Darlan was quite a near run thing. He left Toulon on November the 7th to visit his son who was suffering an attack of Polio in Algiers. As a result he was in Algiers during the Uprising the following day, and captured by the French resistance in the November 8th Putch. This would lead to him defecting to the allies and subsequently being accepted as Leader of the Free French (sort of) until he was assassinated in December.
But let's say that his son does not have the polio attack? Darlan remains in Toulon during the events of November 8th and is not captured by the Allies. This puts him in a much different position as the Germans execute Case Anton. Instead of meekly calling for the French fleet to defect, Darlan can order his subordinates in person. If anyone had the clout to get the Vichy French fleet out of Toulon, it would be Darlan. So instead of being scuttled in November, the fleet sails out relatively unopposed (a few air attacks, perhaps a few ships sunk) and meets up with the Allies in North Africa.
Now this gives Darlan even more clout than he had in OTL and Eisenhower will no doubt recognize his self-appointment as head of French North and West Africa, and the assumption of the de-facto leadership of the Free French. Darlan will in addition command his fleet while Giraud will command the army. All of this to the dismay of Charles De Gaulle.
Now undoubtedly, there will be an attempt(s) to assassinate Darlan in TTL like in OTL. Lets assume that in TTL for the sake of the scenario, and due to perhaps more security around Darlan himself (say French Marines) these attempts fail. Furthermore let's assume that following the failure of these attempts on Darlan's life, the allies agree to look the other way when Darlan & co. "take care of" the troublesome De Gaulle and recognize Darlan's leadership of the Free French in exchange for him rolling back some of his more fascist policies. None of the allies particularly like the situation, but it's a political expediency, and they weren't all the biggest fans of De Gaulle in the first place.
Now by December of 1942 you've got a much stronger (albeit somewhat divided) Free French force under Darlan (navy) and Giraud (army). The addition of the Vichy French Fleet won't affect things too much ( a few more battleships supporting Husky, Dragoon, D-Day perhaps). How will the invasion of France play out in TTL? Any changes? What about post-war France?