French assistance preceded Saratoga, although there wasn't a formal alliance. Many French volunteers fought for the colonists prior to Saratoga, including Lafayette. The whole reason the US issued a "Declaration of Independence" was at French insistence that they make some kind of declaration of intent. Clandestine support proceeded apace from 1776 onward. At any rate Saratoga was in 1777. The alliance was formalized in 1778 not because of Saratoga but because the French wanted to prevent US-British reconciliation. The British offered peace terms early on in 1778 and again in May of that same year.
In the meantime what had been preventing an earlier alliance was reports of British victories against the colonists, particularly Brooklyn, Brandywine, Ticonderoga, and Germantown.
The French fought the British at Pondicherry, Onessant, fought the largest battle of war at Gibaltrar for 4 years, defeated the British at Grenada, defeated the British at Minorca, fought at Cape Henry, defeated the British at Lynn Haven Bay, fought at Trincomalee, and defeated the British at Cuddalore.