When did the French become allies to the Patriots during the Revolutionary War?

After the Battle of Saratoga, the French decided that the Americans had enough power to win the war and decided to help them. They officially joined them on February 6, 1778. France could easily remember how Great Britain had won the French and Indian War, and France lost allot of territory. France was an enemy of Great Britain. The American Revolution gave France a chance to weaken Great Britain.