Dalmas began in the French Formula Renault series, finishing third in 1983 with three victories. He returned to the championship in 1984, winning six races from twelve starts to take the title. In 1985 he stepped up to French Formula 3, finishing second after winning three races. In 1986 he beat Jean Alesi to claim a dominant championship crown. Having made his International Formula 3000 debut near the end of 1986, Dalmas contested the series with Oreca Motorsport in 1987; wins at Pau and Jarama earned him fifth in the standings.
Towards the end of the 1987 Formula One season, Dalmas joined the Larrousse team, driving its new second entry in the final three races. He outqualified teammate Philippe Alliot on his debut at the Mexican Grand Prix but finished ninth, last of the finishers. At the season finale in Australia, Dalmas finished fifth, but missed out on scoring two championship points because Larrousse had only entered one car for the championship season.
Dalmas remained at Larrousse for 1988. He narrowly missed points twice: he was overtaken by Riccardo Patrese on the final lap of the Monaco Grand Prix, finishing seventh, and placed seventh again at Detroit. He missed the final two races of the season after being diagnosed with Legionellosis. The 1989 campaign was turbulent: Dalmas qualified for only one of the first six races before leaving Larrousse for AGS. With AGS he was eliminated in pre-qualifying in each of the season's final nine races, sharing that fate with teammate Gabriele Tarquini. In 1990 he qualified for five of the year's sixteen events, with a best result of ninth in Spain.
In 1991, Dalmas joined the Peugeot Sport works team, partnering Keke Rosberg in the Sportscar World Championship at the wheel of a Peugeot 905. The pair retired from the opening five events of the season. After the updated 905 Evo 1 Bis was introduced, Dalmas and Rosberg won back-to-back at Magny-Cours and Mexico City before retiring from the season finale.
In 1992, the final year of the World Sportscar Championship, Dalmas partnered Derek Warwick in the No. 1 905 Evo entry. They finished second at Monza — Dalmas having flipped his car with two laps to go due to fading brakes — and won at Silverstone. At the 24 Hours of Le Mans, Dalmas, Warwick, and Mark Blundell built a dominant lead during the night and early morning. Despite losing three laps with an ignition failure in the morning, the trio drove home to victory. Dalmas and Warwick clinched the truncated WSC title by winning at Suzuka.
At the 1993 24 Hours of Le Mans, Dalmas was joined at Peugeot by Teo Fabi and Thierry Boutsen; the trio finished second in a Peugeot podium lockout. Away from Le Mans in 1993, Dalmas participated in touring car events and finished second at the Spa 24 Hours alongside Michael Bartels and Harald Grohs.
1994 — Dauer 962 Le Mans Porsche: Dalmas moved into touring car racing full-time in 1994, contesting the French Supertouring Championship and placing fourth with two victories at Dijon. At Le Mans he partnered former winner Hurley Haywood and Mauro Baldi in the GT1-class Dauer 962 Le Mans Porsche. The team fought for victory thanks to its larger fuel capacity, but Dalmas ran out of fuel on pit entry and had to be pushed to his pit box by the marshals. Despite nursing the car home with a fragile driveshaft, Dalmas and his teammates profited from Toyota's problems to win the race overall — his second Le Mans win.
1995 — McLaren F1 GTR: For 1995 Dalmas drove a McLaren F1 GTR alongside JJ Lehto and Masanori Sekiya. They won the race, with a late charge from Bob Wollek — who unlapped himself from Dalmas in the final hour — ending up unsuccessful. Dalmas later described the GTR as "not a simple car to drive." This was his third Le Mans victory from four starts.
1999 — BMW: From 1999 onwards Dalmas concentrated on Le Mans. He switched to BMW and made his brand debut at the 1999 12 Hours of Sebring. At the 1999 24 Hours of Le Mans, Dalmas raced alongside Pierluigi Martini and Joachim Winkelhock. Dalmas was involved in a battle for the race lead with the No. 3 Toyota from Sunday morning, but the chase ended with a late puncture for the Toyota, allowing Dalmas to coast to his fourth Le Mans victory.
Later in 1994, Dalmas returned to Formula One, driving two races for Larrousse. He narrowly outqualified teammate Érik Comas at Monza but retired on lap 19 after spinning off. In Portugal, Dalmas was outqualified by Comas and finished fourteenth, his final Formula One race.
In 1996, Dalmas drove for Opel in the rebranded International Touring Car Championship, finishing seventeenth overall with no podium finishes. At Le Mans that year he drove a Porsche 911 GT1 with Karl Wendlinger and Scott Goodyear, qualifying second but suffering a ten-minute repair stop in the seventh hour after going off at Mulsanne; the trio still recovered to third overall.
In 1997, Dalmas competed in the newly formed FIA GT Championship, initially for Porsche privateer Roock Racing before joining Bob Wollek in the works team's No. 7 entry from the fourth round. He scored third places at Spa and Mugello and second at Laguna Seca. Away from Le Mans, Dalmas triumphed at the 1997 12 Hours of Sebring in a Ferrari 333 SP.
During the 1998 FIA GT Championship, Dalmas partnered Allan McNish on a run of six successive podium finishes, ending third in the standings. His Le Mans ended prematurely when teammate Michele Alboreto suffered an ignition failure. Dalmas also flipped his Porsche at the Petit Le Mans event that year in a blowover incident.
Dalmas's final professional motor race was the 2002 24 Hours of Le Mans, piloting an Audi R8 for Team Goh; he finished seventh overall. Across his twelve years competing at Le Mans, Dalmas never had the same teammate twice.
In the 2010s, Dalmas served as special driving advisor and Safety Car driver for the FIA World Endurance Championship. He tested the Porsche 919 Hybrid and Toyota TS050 Hybrid LMP1 chassis during the 2016 post-season test. Dalmas was named Grand Marshal for the 2025 24 Hours of Le Mans and stepped back from his driving advisor and Safety Car driver roles at the end of the 2025 FIA World Endurance Championship season.
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