Pierre was born at Berc in the Département of Lozere on the 1st October, 1903. He trained as an engineer and by the early 1920s he was living in the Rue du Bournou in Eze, just inland between Monaco and Beaulieu Sur Mer in the South of France.
As a young man he got to know the American composer Samuel Barlow who moved to Eze from New York in the early 1920s. Barlow restored La Maison des Riquiers, also know as the Château Riquier, and also built a garage in La Place de la Colette for his Mathis (French manufacturer between 1905 and 1946) and Bugatti Royale. It was a large building which also included accommodation for staff. Pierre loved cars and acted as Barlow's chauffeur whenever one was required.
Veyron's first love was engineering which he studied at University however his friend Albert Divo, a successful Grand prix driver, persuaded him to have a go at racing and in 1930 he started racing with an EHP sports car with which he took class wins in the hillclimbs at La Turbie and L’Esterel and also finished 2nd in the 1,500cc class in the 1930 Grand Prix d'Oranie on the Arcole track in Algeria. Divo introduced Pierre to André Vagniez, a wealthy industrialist from Amiens, who offered him financial support (Vagniez himself tried racing in the mid 1930s) and in 1931 he purchased a Bugatti Type 37A for him.
Veyron already knew Ettore Bugatti and had put the garage in Eze at the disposal of the works team at the time of the first Monaco Grand Prix in 1929. In 1931 he drove the Type 37A Bugatti in Voiturette races. He started by finishing second in the Grand Prix de Tunisie behind Ernesto Maserati, but then posted a DNF at St Raphael in the Circuit d'Esterel Plage. He then won the 1,500cc class at the Grand Prix de Genève beating Lurani and Wimille and also finished third in the Circuit du Dauphiné Voiturette in Grenoble and second in the Grand Prix at Comminges.
He switched to racing a Maserati 26C in 1932 and once again finished second in the voiturette class in the Grand Prix de Tunisie. This was followed by another second in the Grand Prix d'Oranie before he took his second win, this time in the Grand Prix de Casablanca at Anfa, Morocco. He backed that up with another win in the Grand Prix de Lorraine, a second in the Circuit de Vitesse de Nice and another victory in the Grand Prix du Comminges. He finished a very successful season with second in the Masarykuv Okruh at Brno in Czechoslovakia. It was in 1932 that Ettore Bugatti’s son Jean offered Pierre a job as test driver and development engineer.
Thus in 1933 he returned to racing a Bugatti as part of the works team and, armed with the latest Type 51A Bugatti, he won the Avusrennen, the Miedzynarodowe Okrezne Wyscigi Automobilowe Grand Prix Lwowa, which is other wise know by it's shorter title of the Grand Prix of Lwow in Poland, and the voiturette race at the Grand Prix de l'Albigeois at Albi. He also finished 2nd in the Grand Prix de La Baule and 3rd in the Eifelrennen and at Dieppe.
Another season with Bugatti followed and once again took a number of wins including the races at AVUS and Albi. He finished second in the Prix de Berne behind Dick Seaman and also drove a Type 51 Bugatti in the Grand Prix de l'Albigeois finishing third overall beating Raymond Sommer in a Maserati 8CM into fourth. In the voiturette race there he took the win. That year he made his first trip to Le mans for the 24 hour race. Teamed with Roger Labric in a Bugatti T50S they went out with engine problems after 73 laps.
He had another very successful season in 1935 with a second in the in the Grand Prix des Frontiéres. He won the Voiturette Grand Prix d'Lorraine at Nacy in France after Cholmondley-Tapper who, despite colliding with Mestivier at the start, held a 10 minute lead after two and a half hours racing. Unfortunately for him he developed brake problems and spun leaving Pierre to take the win. He was also slightly lucky at Albi where the race was run in 2 heats with times added for final result. He was second in the first heat and in the second Barbieri, who won the first, was leading when he retired with engine failure, leaving Veyron to take the second heat and the overall win, Bugatti's last major victory. He was third in Dieppe and retired from the Prix de Berne with fuel feed problems. he finished the season in Czechoslovakia with second in the Masarykuv Okruh at Brno. At Le Mans he once again drove with Roger Labric in his Bugatti T50S and, once again, they retired.
In 1936 Bugatti concentrated on sports car races finishing 6th in the Grand Prix de l'ACF, a 1,000 km race at Montlhery, driving with 'Williams'. He also finished 4th in the Grand Prix de la Marne driving a Bugatti T57G, a car in which he did much of the development work. He did race a Bugatti T51A in the voiturette race at Albi finishing 2nd behind Bira. He drove a Bugatti Type 57TT with Lucien Wurmser in the Paris-Nice Rally in April that year and later Ettore gave the car to him as a present. However it was crashed and returned to the factory where it was rebuilt as a special gift for Ettore himself.
At Le Mans in 1937 he failed to finish yet again with Roger Labric, now with a Bugatti T57G. He missed the race in 1938 but in 1939 came his greatest triumph when he took the win with Jean-Pierre Wimille in the Bugatti T57C 'Tank' at a record speed.
Upon the outbreak of WW2 he took his wife and family to the railway station at Belfort and headed for the Basque country and safety. However he was called up as a reservist and served as a quartermaster in an artillery regiment until France fell in June, 1940. He subsequently joined the French Resistance in a group that involved fellow racing drivers Robert Benoit, Jean-Pierre Wimille and 'Williams'. In 1945, Veyron received the Croix de Guerre for his actions during the occupation.
After the war Veyron restricted his racing to Le Mans though he did race in the Paris 12 Hour race in 1949 and 1950 when he finished 4th with Sacha Gordine in a Gordini TMM, and the Spa 24 Hour race in 1949 when he failed to finish driving a works Gordini T15S with Trintignant. All his post war attempts at Le Mans (1949, 1950, 1951, 1952 and 1953) failed to finish.
He died in Eze in 1970.