Panis was born in Oullins, Lyon, and began his career in karting before working through French junior categories. He won a Formula Renault championship in 1989 and finished second in French Formula 3 in 1991. Those results were solid but not spectacular, and he required a further season or two in the feeder system before finding his way into Formula 3000.
Panis entered the International Formula 3000 series and won the championship in 1993. The title earned him the Formula One seat he was seeking, and Ligier signed him for the 1994 season.
The 27-year-old Panis made his F1 debut with Ligier in Brazil in 1994, finishing eleventh. He earned a surprise second place at Hockenheim that year and finished eleventh in the championship. In 1995, he added another second place, this time at the Australian Grand Prix, finishing eighth in the standings.
His most celebrated moment came at the 1996 Monaco Grand Prix. Starting fourteenth on a wet track, Panis worked his way through the field as other drivers retired, timing his switch to slick tyres perfectly and overtaking Eddie Irvine at the Loews Hairpin. When Damon Hill and Jean Alesi both suffered mechanical failures, Panis inherited the lead and held off a late charge from David Coulthard to win. It was only one of three cars to reach the finish, and it represented Ligier's first victory in fifteen years and the first French victory in a French car at Monaco in 66 years.
Panis drove for the Prost team (formerly Ligier, purchased by Alain Prost) in 1997, starting the season strongly with a podium at Brazil and second place in Spain. At the 1997 Canadian Grand Prix he broke both legs in a high-speed accident, missing seven rounds before returning for the final three races of the season. Despite missing half the season, he still finished ninth in the championship with 16 points.
In 1998, with pins still in his legs from the surgery, Panis struggled to score a point for Prost. His fortunes improved slightly in 1999 with a more competitive car, but strategic errors limited his results. He tested for McLaren after leaving Prost, regularly matching the times of David Coulthard and Mika Hakkinen, before landing a drive with BAR for 2001 and 2002, scoring eight points across two seasons. He moved to Toyota for 2003 and 2004, contributing experience but limited results, and retired from F1 after the 2004 Japanese Grand Prix, later working as a Toyota test driver through 2006.
Panis returned to racing in 2008 in the Le Mans Series with the Oreca Courage team, finishing fifth at the 24 Hours of Le Mans in both 2009 and 2011. In 2016, he co-founded the Panis Barthez Competition sports car team alongside footballer-turned-driver Fabien Barthez. After Barthez departed at the end of 2019, the renamed Panis Racing operation continued to grow, earning back-to-back LMP2 podiums at Le Mans in 2020 and 2021, and eventually winning the 2025 ELMS LMP2 championship.
Panis is remembered primarily for his 1996 Monaco win, one of the most unlikely victories in Formula One history, but his Formula 3000 title was the foundation on which that career was built. As a team owner he demonstrated longevity and ambition that extended well beyond his driving years, with Panis Racing becoming a credible force in European endurance racing.