Fort Greene is a United States Army Reserve installation in the Point Judith area of Narragansett, Rhode Island. During World War II this was a coastal defense fort, and together with Fort Church in Little Compton, it superseded all previous heavy gun defenses in the Harbor Defenses of Narragansett Bay. It is named for General Nathanael Greene of the …Fort Greene is a United States Army Reserve installation in the Point Judith area of Narragansett, Rhode Island. During World War II this was a coastal defense fort, and together with Fort Church in Little Compton, it superseded all previous heavy gun defenses in the Harbor Defenses of Narragansett Bay. It is named for General Nathanael Greene of the Revolutionary War, who was born in Rhode Island.