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Right - and as you said, the French saw that but it was only after BF was on them constantly.

The French goal was to weaken Britain, both to keep it from getting too powerful and to exact revenge for the defeat in the Seven Years' War. After the American capture of the British invasion army at Saratoga in 1777, and after the French navy had been built up, France was ready. In 1778 France recognized the United States of America as a sovereign nation, signed a military alliance, went to war with Britain, built coalitions with the Netherlands and Spain that kept Britain without a significant ally of its own, provided the Americans with grants, arms and loans, sent a combat army to serve under George Washington, and sent a navy that prevented the second British army from escaping from Yorktown in 1781. In all, the French spent about 1.3 billion livres (in modern currency, approximately thirteen billion U.S. dollars) to support the Americans directly, not including the money it spent fighting Britain on land and sea outside the United States.

So basically France had an alterior motive in helping American independence.