As an amateur, Jean Goujon’s career highlight was at the 1936 Olympics, where he was a member of the French pursuit team that won a gold medal. At those Olympics Goujon also competed in the road race, finishing with a large pack who were all placed joint 16th. As the last of the Frenchmen, Goujon was the non-scoring member of the French road race team that won a gold medal. As an amateur, he finished sixth at the 1934 World Road Championships, won Paris-Reims in 1933, was second at the 1933 Paris-Chauny race, and was second in 1935 and third in 1933 at Paris-Évreux.
Goujon turned professional shortly after the 1936 Olympics and rode until 1949. Goujon was 35th overall at the 1937 Tour de France, won 1937 Paris-Verdun, was second at 1938 Tour de l’Oise (now named Tour de Picardie) and won Prix Goullet-Fogler in 1937 and 1940, Prix Dupré-Lapize in 1938, Prix de l’Ouverture in 1940, and Prix Houlier-Comès in 1941.