René Le Grevès was the winner of several road races as an amateur. At the 1930 World Championships he just missed a medal, placing fourth in the road race. He turned professional after winning the silver medal in the team pursuit at the Los Angeles Games and took part in the Tour de France in 1933-36 and 1939, winning a total of 16 stages, with six in 1936 and in 1935, Le Grevès won three consecutive stages. That year also saw him with his best GC placement of 15th. He was said to be one of the best sprinters in the Tour and achieved further success in many classic races, winning at Paris-Tours in 1935. He was French road racing champion in 1936. In 1937 Le Grevès founded a bicycle shop that has been continued by his family to this day. He died in February 1946 in Saint-Gervais-les-Bains in a skiing accident.