He was admitted to study at Polytechnique in 1940 but left France with his family to escape the anti-Jewish persecutions.
Elkann continued his studies in the United States and received a Bachelor of Science degree from Columbia Business School in 1943 while living at The Pierre hotel in New York City.
He was also the president of the Consistoire israélite de Paris from 1967 to 1982, then chairman of the Israelite Central Consistory of France from 1982 to 1992, and interim president of the Conseil Représentatif des Institutions Juives de France (CRIF) in late 1982, replacing Alain de Rothschild, who died of a heart attack in October 1982.
As quoted by the Chief Rabbi, Michel Gugenheim, Elkann told the leader of Reform Judaism in the United States, Alexander Schindler: "The only difference between you and me, Mr. rabbi, is that I violate the law, but I do not change it, and you want to change the law."
He was also the vice president of the France-Israel Chamber of Commerce, the chairman of the Association de coopération économique France-Israël, Haifa Technion governor, administrator of Yabné school, administrator of the Alliance Israelite Universelle, and vice chairman of the Social Action Committee Israelite de Paris (CASIP).