Gachot was the son of a French European Commission official. He began karting at the relatively old age of 15. In 1983, he attended Winfield School, a well-known racing-driving school in France. After this, he focussed on his racing career, competing first in the Formula Ford 1600 series. By 1986, he had won the British Formula Ford championship.

In 1987, Gachot joined the British Formula 3 series, finishing second in the championship for the West Surrey Racing team. In 1988, he switched to the Formula 3000 series, but met some success. In 1989, he entered the storied world of Formula One, driving for the newly-formed Onyx team. Although his performances were promising, after making statements in the press which caused the ire of his erratic team boss, Gachot lost his drive before the season's end. Instead, he switched in 1990 to the Subaru-powered Coloni team, with little success.

In 1991, he joined the Jordan Grand Prix racing team, helping them to fifth in the constructor championship. However, his season was cut short by a two-month prison stint, received for spraying CS gas on a London taxicab driver after a traffic altercation. (His race seat was filled, momentarily at least, by then-unknown Michael Schumacher, who was just making his F1 debut). When he was finally released from prison after 2 months, he had missed 4 Grand Prix (including his home Grand Prix in Belgium). The Jordan Grand Prix racing team was not interested in returning his seat(which was given to Alessandro Zanardi) for the last two races of the season in Japan and Australia. Finally, he was able to dispute the last Grand Prix of that season with Larrousse replacing Eric Bernard but he failed to qualify. Gachot then spent the complete 1992 season with the Larrousse team, scoring 1 point in the Monaco Grand Prix where he finished in 6th place.

Gachot spent the next several years racing in various formulae. He was involved in the Pacific Racing F1 team behind the scenes, as well as driving for them for most of their two-year existence. The high point of Gachot's career is winning the renowned 24 hours of Le Mans sports car race in 1991 in a Mazda (with co-drivers Johnny Herbert and Volker Weidler). In later years, Gachot's career included marketing "Hype", a high-energy beverage, as well as running an F1 website.

Gachot competed in a total of 47 grand prix for eight different teams. He never won a race, but he did score five championship points during his F1 career, and even recorded the fastest lap of the 1991 Hungarian Grand Prix for Jordan.