Behra began racing motorcycles, using a Terrot that Jean had prepared for him; with it he scored his first three victories. He transitioned to car racing and partnered Georges Houel in the 1954 Giro d'Italia, a 10-day, 5,763 km (3,581 mi) road rally, driving an Alfa Romeo to tenth overall and second in class. In 1955 he took part in the Monte Carlo Rally and two further rallies in Belgium. He reunited with Houel to drive a Maserati A6GCS at the Supercortemaggiore Grand Prix at Monza, finishing twelfth overall, behind the winning Maserati 300S of brother Jean and Luigi Musso.
Through 1956 and 1957, Behra continued racing alongside family members and regular co-drivers. He served as Jean's co-driver in the Tour de France Automobile in 1956, finishing fifth overall. In 1957, partnering Léon Coulibeuf, he entered two rounds of the World Sportscar Championship — Le Mans and the Swedish round — in a Maserati 200S, retiring from both. At the Swedish event he was pushed into a ditch by a spinning competitor. The same year he drove with Christian Boulan to twenty-second overall (fourth in class) at the 12 Hours of Reims.
The 1958 24 Hours of Le Mans brought an unexpected opportunity. The North American Racing Team had entered brothers Pedro and Ricardo Rodríguez in a Ferrari 500 TR, but the ACO judged the 16-year-old Ricardo too young to compete and Behra replaced him. He and Pedro Rodríguez outlasted NART's other two entries before retiring in the twelfth hour with a holed radiator. Behra enjoyed a productive 1958 in a Porsche 356, winning his class alongside Pierre Marx at the Trophée d'Auvergne and taking a further class win at the Coupes du Salon.
Throughout 1959, brother Jean was developing a Formula Two car under the Behra-Porsche marque while also driving for Scuderia Ferrari — a relationship famously acrimonious. Jean entered a Porsche for the 1959 Monaco Grand Prix with Maria Teresa de Filippis at the wheel and José listed as reserve; de Filippis did not qualify. Jean was dismissed from Ferrari after the French Grand Prix, entered his own car to the German Grand Prix, and crashed fatally in the supporting sportscar race. José overcame the loss and continued to race.
Behra raced a Jaguar Mk II throughout 1960, opening the year with a class win and third overall in the Alpine Rally before retiring from the Trophée d'Auvergne and the Liège–Rome–Liège. He achieved his career-best Monte Carlo Rally finish of eighth place in 1961. In 1962 he retired from the 24 Hours of Le Mans with gearbox failure. He co-piloted Jean Guichet to outright victory in the 1963 Tour de France Automobile, then drove to second in the GT1.0 class in 1964. In 1969 he co-drove with Jean-François Piot in the Alpine Rally, where illness forced retirement, before the pair won their class in the Tour de France that year. His final Tour de France appearance came in 1970, co-driving with Jean-Claude Andruet in a new Ligier JS1 sports prototype; both cars retired with engine troubles.
During the 1960s, Behra imported American cars to the Paris region in association with Guy Ligier. He relocated to Puteaux in 1972 and became a Ford dealer there, retiring in 1990 and handing the business to his adopted son Eric. In 1968, Behra joined Ligier and Jo Schlesser to found the Formula Two team Écurie Intersport SA, which entered two cars for Ligier and Schlesser in the European Formula Two Championship. The team's season ended abruptly when Schlesser was killed during the 1968 French Grand Prix, after which Ligier immediately retired as a driver to concentrate on building cars.