Thévenet was born to a farming family in Burgundy. He started competing as an amateur in 1963 and was champion of Burgundy in 1965 and 1966 and French junior champion in 1968. During 1968, he rode for the amateur team of Jean de Gribaldy, Cafés Ravis-Wolhauser-de Gribaldy, which won the amateur Route de France. After that Thévenet did his military service in 1969. He turned professional with Peugeot-BP-Michelin in 1970. He entered the Tour de France for the first time in 1970, winning a mountain stage ending at the resort of La Mongie. In the 1972 Tour he crashed badly on a descent and was temporarily amnesic. As he began to regain his memory, he looked down at his own Peugeot jersey and wondered whether he might be a cyclist. On recognizing the team car, he exclaimed: “I’m riding the Tour de France!” He refused to abandon the race and four days later won a stage over Mont Ventoux. In the 1973 Tour, he finished second, behind Luis Ocaña, but in 1974 he did not enter the Tour due to illness.
In the 1975 Tour, Thévenet attacked Eddy Merckx on the Col d'Izoard. Merckx, who was suffering back pain and the effects of a punch from a fan, fought back but lost the lead and never regained it. Thévenet went on to win the Tour, which that year finished on the Champs-Élysées for the first time. Merckx finished second, three minutes behind.
Thévenet won his second and last Tour in 1977. In the same year he tested positive for doping after Paris-Nice and that winter he was hospitalized with a liver ailment which he attributed to long-term use of steroids. Several months later Thévenet lined up for the 1978 Tour de France but had to abandon the second mountain stage in an ambulance. He left the Peugeot cycling team after 1979 and signed for the Spanish team Teka, where he won two races and a six days race with the Australian rider Danny Clark. He returned to a French team in his final year, 1981, where he won a stage in the Circuit de la Sarthe. He retired from cycling, made a public admission of his steroid use and called for an end to performance-enhancing drugs in the sport. He was once asked whether it was hard being a racing cyclist; his reply was that being a French farmer was harder. Thévenet returned to the sport as a directeur sportif in 1984 of the La Redoute team of Stephen Roche and after that he was the directeur sportif of the R.M.O. team in 1986 and 1987.
In retirement, Thévenet became a television commentator and opened a company selling cycling clothes bearing his name.