Panis began in karting before progressing through French junior formulae. He won the Formula Renault championship in 1989 and finished second in French Formula 3 in 1991. His move to Formula 3000 proved fruitful: he won the championship in 1993, earning a Formula One drive with the Ligier team for 1994.
Panis made his Formula One debut at the 1994 Brazilian Grand Prix, finishing eleventh. His first notable result came later that season with a surprise second place at Hockenheim. In 1995 he achieved another second place at the Australian Grand Prix and added several fourth-place finishes, ending the year eighth in the championship.
The defining moment of Panis's career came at the 1996 Monaco Grand Prix. Starting fourteenth on a wet track, he picked his way through the field on the narrow street circuit, passing Martin Brundle, Mika Häkkinen, and Johnny Herbert. He timed a switch to slick tyres perfectly, overtook Eddie Irvine at the Loews Hairpin, and inherited the lead when both the leading Williams of Damon Hill and the Benetton of Jean Alesi suffered terminal mechanical failures. Panis held off a late challenge from David Coulthard to win, with only three cars finishing the race. The victory was Ligier's first win in fifteen years and the last of the team's history. It was also the first French victory in a French car at Monaco in 66 years.
For 1997, Panis remained with the team after Alain Prost purchased Ligier and renamed it. On Bridgestone tyres, he helped the tyre manufacturer claim its first Formula One podium at the Brazilian Grand Prix and finished second in Spain, where a seven-lap delay behind backmarkers during lapping operations denied him a likely victory. After six rounds he stood third in the Drivers' Championship. At the 1997 Canadian Grand Prix, a high-speed accident resulted in fractures to both legs, sidelining him for seven races. Jarno Trulli deputised during his absence. Despite missing half the season, Panis recovered to take ninth in the championship with sixteen points.
The 1998 season proved deeply difficult. The Prost car was uncompetitive and leg pins remaining from his 1997 surgery further limited his performance; he failed to score a single point. Results improved somewhat in 1999 with a stronger car: Panis claimed sixth places in Brazil and at Hockenheim and qualified as high as third at the French Grand Prix. However, strategic errors and misfortune kept his points total modest and he parted ways with Prost at season's end.
After serving as a McLaren test driver — where his pace regularly matched that of regulars David Coulthard and double champion Mika Häkkinen — Panis joined British American Racing for 2001. The team was not as competitive as he had hoped. Over two seasons at BAR he finished fourteenth in the championship both years, scoring a total of eight points. His best result with the team was fourth in Brazil.
Panis moved to Toyota for 2003, bringing experience to a team in only its second season. His handling of the new one-lap qualifying format helped early results, but he again ended the year fifteenth with six points. He remained with Toyota in 2004 — his tenth Formula One season — and matched the same points tally before announcing his retirement ahead of the Japanese Grand Prix. He was the oldest active Formula One driver at 37. Ricardo Zonta replaced him for the final race in Brazil. Panis continued as a Toyota test driver through 2006, making his last competitive Formula One appearance as nominated third driver at the 2005 French Grand Prix. He formally retired from all Formula One duties in December 2006.
Panis returned to racing in 2008 with the Oreca Courage team in the Le Mans Series. He finished fifth at the 24 Hours of Le Mans in both 2009 and 2011. In 2016 he co-founded Panis Barthez Compétition alongside footballer-turned-racing driver Fabien Barthez, entering cars in the European Le Mans Series and the Blancpain GT Series. After Barthez stepped down at the end of 2019 the team continued as Panis Racing, claiming back-to-back LMP2 class podiums at the 24 Hours of Le Mans in 2020 and 2021. In 2025 the team won the European Le Mans Series LMP2 title.
Panis is remembered principally for his Monaco victory, widely considered one of the most unexpected wins in Formula One history given his lowly grid position and the field he dispatched. His racecraft was highly regarded; Häkkinen reportedly expressed particular disappointment when Panis left McLaren's testing programme to return to full-time racing. As a team owner, Panis has established a lasting presence in European endurance racing, and his son Aurélien Panis has followed him into professional motorsport.