Cut the Free French forces out of the picture and generally have little in the way of a French government in exile of any form. Not only does this solidify the legitimacy of Vichy, but it also makes its leaders (relatively) more attractive to Allied agents who might convince them to flip give the right circumstances. Have a military build-up in North Africa that looks like its going to go after Italy, but through Overlord-like deception operations and pre-reached talks with the resistance, elements of the Vichy military and government, ect. in the South (Preferably during a period when the Germans are getting wollaped hard in the East), get the South to "coup" and allowed Allied forces into the south of France. Since large numbers of the German units in France are re-cooperating or static, and if you still have sufficent forces across the channel to make Germany have to keep an eye cocked towards Britain, with friendly ports and sufficient speed that the Germans can't respond fast enough.