What long-term impact did the Battle of Saratoga have that helped the Americans win the Revolutionary War? Responses The colonial victory convinced France to join the American Revolution and fight for the colonies The colonial victory convinced France to join the American Revolution and fight for the colonies The territory gained through the battle allowed colonial supply lines to expand The territory gained through the battle allowed colonial supply lines to expand Spain withdrew their support for the British after the British surrender Spain withdrew their support for the British after the British surrender British troops were reduced significantly enough that they never recovered