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hats Entry into the war Main article: Franco-American alliance

Surrender of General Burgoyne at the Battle of Saratoga, by John Trumbull, 1822. The British had taken Philadelphia in 1777, but American victory at the Battle of Saratoga brought back hope to the Patriots and enthusiasm in France. The army of Burgoyne surrendered to American forces after Saratoga, and France realized that the Thirteen Colonies could be victorious. Consequently, King Louis directed Vergennes to negotiate an alliance with the Americans. France formally recognized the United States on February 6, 1778, with the signing of the Treaty of Alliance. War followed not long after, when Britain declared war on France on March 17, 1778. The British naval force, then the largest fleet afloat, and French fleet confronted each other from the beginning. The British avoided intercepting a French fleet that left Toulon under the comte d'Estaing in April for North America, fearing the French fleet at Brest might then be used to launch an invasion of Britain. France had kept the Brest fleet to protect commercial shipping in European waters, and it sailed out only after a British fleet was confirmed to have left in pursuit of d'Estaing, thus weakening the British Channel fleet. In spite of this reduction the British fleet still outnumbered the French fleet at Brest, and Admiral d'Orvilliers was instructed to avoid combat when he sailed in July. D'Orvilliers met the fleet of Admiral Augustus Keppel in the indecisive Battle of Ushant on July 27, after which both fleets returned to port for repairs. France did consider the landing of 40,000 men in the nearby British Isles, but abandoned the idea because of logistical issues. On the continent, France was protected through its alliance with Austria, which, even if it did not take part in the American Revolutionary War, affirmed its diplomatic support of France. Other nations in Europe at first refused to openly join the war, but both Spain and the Dutch Republic gave unofficial support to the American cause. Vergennes was able to convince the Spanish to formally enter the war in 1779, and Britain declared war on the Dutch Republic in 1780 over claims of Dutch violations of neutrality.