Lanzmann was born on 27 November 1925 in Paris, France, the son of Paulette () and Armand Lanzmann. His family was Jewish, and had immigrated to France from Eastern Europe. He was the brother of writer Jacques Lanzmann. Lanzmann attended the in Clermont-Ferrand. While his family disguised their identity and went into hiding during World War II, he joined the French resistance at the age of 17, along with his father and brother, and fought in Auvergne. Lanzmann opposed the French war in Algeria and signed the 1960 antiwar petition Manifesto of the 121.