The son of a doctor, Galley was born in Paris on January 11, 1921. During the Fall of France in 1940, Galley was able to escape to the United Kingdom disguised as a Polish soldier. He joined the Free French Forces and was sent to North Africa, including the Battle of El Alamein. Galley was next stationed within General Philippe Leclerc de Hauteclocque's 2nd Armored Division, through which he participated in the Liberation of Paris and the Western Allied invasion of Germany. Galley later married General Leclerc de Hauteclocque's daughter, Jeanne Leclerc de Hauteclocque, following the end of World War II.