He was born in Nantes. He studied at École Normale Supérieure from 1926 to 1929. He received his Ph.D. in 1933. From 1938 to 1939 he was professor at the University of Nancy. He did not join up to the Bourbaki group, although he was close with its founders.
His main work in topology was carried out while he was in a prisoner of war camp in Edelbach, Austria from 1940 to 1945. He concealed his expertise on differential equations, fearing that its connections with applied mathematics could lead him to be asked to do war work.
Leray's work of this period proved seminal. It originated, together, the ideas of spectral sequence and sheaf. These were subsequently developed by many others, each separately becoming an important tool in homological algebra.
He returned to work on partial differential equations from about 1950.
He was awarded the Malaxa Prize (Romania, 1938), the Grand Prix in mathematical sciences (French Academy of Sciences, 1940), the Feltrinelli Prize (Accademia dei Lincei, 1971), the Wolf Prize in Mathematics (Israel, 1979), and the Lomonosov Gold Medal (Moscow, 1988).