France provided military aid to the United States during the revolution because they wanted to defeat Britain. France and Britain have long been rivalries, and enemies in the past, this being one of their many militaristic meetings. The French saw the American Revolution as an opportunity to embarrass the British and took advantage.

France was still very grouchy at loosing the 7 years war, and so this was the perfect opportunity to get back at Britain. Kind of a stupid idea though considering it practically caused the French Revolution