Which 1777 battles persuaded France to ally formally with the American revolutionaries?

The Battles of Saratoga persuaded France to ally formally with the American revolutionaries.

The two major battles were fought near Saratoga, New York, on September 19 and October 7, 1777. American forces under General Horatio Gates opposed a British army commanded by General John Burgoyne, whose campaign aimed to control the Hudson River Valley and separate New England from the other colonies.

The second battle ended in a decisive American victory, and Burgoyne surrendered his army on October 17, 1777. The outcome demonstrated that the American forces could defeat a major British field army, changing European calculations about the likely result of the war.

France signed the Treaty of Alliance with the United States on February 6, 1778. French military, naval, financial, and material support became crucial to the American cause, including the naval operations that helped produce the British surrender at Yorktown. Saratoga is therefore often described as a major turning point of the Revolutionary War.