Gottmann was born in Kharkov, Ukraine, Russian Empire. He was the only child of prosperous Jewish parents, Elie Gottmann and Sonia-Fanny Ettinger, who were killed in February 1918, following the Russian Revolution of 1917. He was de facto adopted by his aunt, Emily Gottmann and uncle, Michel Berchin, and escaped with them to Paris in 1921 via Constantinople.