Veyron initially studied engineering at university, where his friend Albert Divo — himself a seasoned racing driver — encouraged him to take up motorsport. Divo introduced Veyron to industrialist André Vagniez, who provided the financial backing to launch his racing career. Vagniez purchased a Bugatti Type 37A for Veyron, and the partnership produced immediate results: Veyron won the 1930 Geneva Grand Prix in that car, announcing himself as a talent worth watching.
The win at Geneva brought Veyron to the attention of Jean Bugatti, son of company founder Ettore Bugatti. In 1932, Jean Bugatti hired Veyron as a test driver and development engineer at the factory, a dual role that placed him at the heart of Bugatti's racing programme. As a works driver, Veyron accumulated a string of victories throughout the mid-1930s, most notably winning the Berlin Avus race in both 1933 and 1934 at the wheel of a Bugatti Type 51A. The Avus circuit's long banked oval rewarded bravery and mechanical sympathy in equal measure, and Veyron's back-to-back victories there reinforced his standing within the team.
The peak of Veyron's racing career came at the 24 Hours of Le Mans in June 1939. Partnered with Jean-Pierre Wimille, Veyron co-drove the Bugatti Type 57S Tank, a streamlined, aerodynamically shaped endurance racer that represented the most advanced competition car Bugatti had produced. The car's enclosed bodywork and low drag profile gave it a decisive speed advantage on the Mulsanne Straight, and the Wimille–Veyron pairing managed the race to take an outright victory. It was Bugatti's last Le Mans win and one of the final major international motorsport events before the outbreak of the Second World War brought racing to a halt across Europe.
During the German occupation of France, Veyron joined the French Resistance, a commitment that carried significant personal risk. For his service, the Republic of France awarded him the Legion of Honour in 1945, the country's highest civilian and military distinction. After the liberation, Veyron returned to racing and continued to compete at a lower intensity through the early 1950s, participating in events until 1953. His post-war focus, however, shifted increasingly toward his family life and his own business interests in oil-drilling technology rather than professional competition.
Pierre Veyron died on 2 November 1970 in Èze, France, at the age of 67. Although his racing record spanned only two decades and was interrupted by the war, his 1939 Le Mans victory with Wimille stands as one of the landmark results in the history of that race. Decades later, Bugatti Automobiles S.A.S. chose to honour Veyron by naming its landmark hypercar, the Bugatti Veyron 16.4, after him — a car that redefined what was technically possible in a road-legal production vehicle and brought his name to a global audience far beyond the boundaries of pre-war motorsport.