British stars were awarded to troops under British command. De Gaulle was ferocious (to the point of Churchill once wishing him guillotined-as did many others before and after) about keeping Free French troops as separate and integral as they could be. I'd be surprised if the French allowed British campaign medals if they were in Free French units. However, we know that Polish, Ethiopian, Norwegian and Czech forces in exile received the campaign stars for certain. I think Dutch troops did as well, as I remember Dutch RAF groups having both types of medals.