Roche had a successful singles and double career. He won one singles Grand Slam tournament, the 1966 French Open at Roland Garros, defeating István Gulyás in the final. He was five times the runner-up at Grand Slam tournaments: the French Championships in 1965 and 1967, losing to Fred Stolle and Roy Emerson respectively, Wimbledon in 1968, losing to Rod Laver, and the US Open in 1969 and 1970, losing to Rod Laver and Ken Rosewall. With compatriot John Newcombe, he won 12 Grand Slam men's doubles tournaments.