Which battle in 1777 convinced France to aid the American cause?

The Battle of Saratoga convinced France to openly aid the American cause in 1777.

The name usually refers to two major engagements in New York: Freeman's Farm on September 19 and Bemis Heights on October 7. The American victory forced British general John Burgoyne to surrender his army on October 17, 1777. It was the first large-scale British army surrender of the Revolutionary War.

Saratoga mattered because it demonstrated that the Continental Army could defeat a major British force, not merely conduct raids or survive defensive battles. France had already been secretly supplying the Americans with weapons, ammunition, money, and other assistance, but the victory persuaded King Louis XVI that the Americans had a realistic chance of winning.

The result was the Treaty of Amity and Commerce and the Treaty of Alliance, signed in February 1778. French military and naval support transformed the rebellion into an international war, stretching Britain's resources across Europe, the Caribbean, and North America. Saratoga is sometimes called a single battle, but historians generally describe the campaign's decisive clashes as the Battles of Saratoga.