Reims yana daya daga cikin kungiyoyin da suka fi nasara a tarihin kwallon kafa na Faransa da suka lashe gasar Ligue 1 guda shida, kofuna biyu na Coupe de France, da biyar na Trophée des champions. Kungiyar ta kuma yi kyau a matakin Turai da suka kammala a matsayin masu tsere a gasar cin kofin Turai a 1956 da 1959 da kuma lashe gasar Latin da Coppa delle Alpi a 1953 da 1977, bi da bi. Duk da haka, tun daga shekarun 1980, Reims sun yi kokari don dawowa zuwa saman su. Kungiyar ta kasance tsakanin Ligue 2 da Championnat National na tsawon shekaru talatin bayan da aka sauke su daga saman jirgin sama a kakar 1978-79.
1956 da kuma 1959