In the 1940s Alfred Eluère was appointed president of the French Rugby Association and of the Comité National Sportif (CNS), replacing Jules Rimet. Eluère held the latter post for 20 years. As a member of the Radical-Socialist Party he was mayor of the Atlantic seaside resort of Hossegor for 37 years, from 1935-72. Eluère worked there as a real estate agent. He was also director of a household appliances business and owner of a restaurant in Paris.
As a rugby player, Eluère earned his first merit as a member of the French military team, when he was stationed as a stenographer in Nantes. After the war, the blindside flanker joined the Sporting Club Universitaire de France, where he became team captain and played until 1923. His cousin Xavier Eluère won a bronze medal as a heavyweight in the 1920 Olympic boxing tournament.