As an amateur cyclist Henri Fin had several podiums in his native France, along with a third-place stage finish at the Scottish Milk Race in 1972. That same year Fin was part of the French quartet that placed 18th in the team time trial at the München Olympics. He then turned professional, but only recorded one career win with victory at the 1975 Wattrelos one-day race in northern France. The following year he rode in the Tour de France, where he was eliminated on stage 10 after not making the time limit.