Roger Veyron was in the prime of his basketball career in the second half of the 1950s, scoring 86 points across 25 matches for the French national team between 1955 and 1959. His most notable appearance came at the 1956 Melbourne Olympics, where his country just missed a podium placement in fourth after losing the bronze medal match to Uruguay. At EuroBasket 1957, he and the French team ranked eighth overall after losing all seven of their games in the final round robin. Domestically, he spent his entire career with CA Saint-Étienne and retired from active competition in the 1960s.
France