I think part of the idea behind the stars was that the Vichy French would be less inclined to shoot at US aircraft than British ones.
After the Armistice in 1940, the Royal Navy sank a large part of the French fleet in North Africa to prevent its possible use by the Nazis. This caused a lot of bad feeling against the British, particularly in the Vichy military.
In the event the Vichy French shot at US aircraft just as much as British ones anyway.