Actually Patton had a real love for the French and was quite indulgent when dealing with them, tho he didn't seem to particularly respect the fighting abilities of the Free French.
Look at how Monty thought of the US Army, yet was in command of a lot of US troops in North West Europe.
I like the idea however, it would help out the Allies, and there should be some way to put troops under control of other nation's HQ's for the allies since they did that quite regularly.