Bernard Baudoux took up fencing in his youth, but World War II limited his ability to compete in his early days. He resumed the sport after the conflict and competed at university-level tournaments while studying at École nationale supérieure agronomique de Montpellier. He made his début at a major international tournament at the 1955 World Fencing Championships, where he made the finals of the individual foil. He then won his only individual national title in that event in 1956 and was selected to represent his country at that year’s Melbourne Olympics. While he ultimately did not start the individual competition, he won silver in the team event alongside Claude Netter, Jacques Lataste, Roger Closset, Christian d’Oriola, and René Coicaud. He was also a reserve in the team épée, but did not compete.
Baudoux’s next stop was the 1957 World Championships, where he captured silver in the team foil tournament. In 1958, he won the team event and also took bronze individually. He underwent an operation in 1959 that effectively ended his sporting days and, by career, he was an agronomist.