Jules Bouquet competed in many sports, but was best known as a wrestler. He was a 7-time French wrestling champion, won the 1919 French Military Championship, and won a bronze medal at the 1919 Inter-Allied Games. In other sports, he competed at the regional level in athletics (in pole vault), cycling (as a sprinter), football, gymnastics, and weightlifting. Bouquet was severely injured by weapons fire in World War I but survived to wrestle at the 1920 Olympics.
Bouquet would later become known for his work in sports administration, particularly in wrestling. He founded the Fédération Française de Lutte Amateur in 1919, and later founded the Fédération Française de Lutte Indépendante in 1935, serving as its President from 1935-37. He helped organize the European Wrestling Championships in 1927, 1929, and 1933, and helped found regional wrestling federations in Bretagne, Normandie, and Touraine. Bouquet also served as technical secretary for the French Olympic Committee from 1924-28.