François Hentges represented the Société de Gymnastique Bonnevoie. He participated in the very first World Artistic Gymnastics Championships in 1903 in Antwerpen winning shared gold in the parallel bars and bronze in the team event and finished ninth in the individual all-around. In 1911, he competed again at the World Championships. Hentges missed the first national trials in January 1912. Nevertheless, after the final trials in June, he was one of 16 gymnasts selected for the Olympics. At the Olympic Games in Stockholm, the team from Luxembourg, including François Hentges, placed fifth and last in the team event of the free system but missed bronze by less than one point in the team event of the European system. In the individual all-around, he placed 23rd. At the Olympic Games in 1924 in Paris, Hentges was a member of the jury. His brother Pierre was also a gymnast and his teammate in Stockholm.
From 1918 until the merger with the city of Luxembourg in 1920, Hentges was on the municipal council of the municipality of Hollerich-Bonnevoie. Subsequently, he was then a member of the municipal council of the city of Luxembourg until 1928. Hentges was a member of the Workers’ and Peasants’ Council, a movement which called for the monarchy in Luxembourg to be replaced by a people’s republic. In 1913, he married Léonie Pauly and worked as a glover.