Delecour began rallying in 1981 in the French national championship. He entered his first major international event, the Monte Carlo Rally, in 1984 driving a Talbot Samba, co-driven by his then girlfriend Anne Chantal Pauwels. He competed in the Peugeot 205 Cup in 1985 and 1986, finishing third in both seasons, which earned him partial works support from Peugeot. By 1989 and 1990 he had a full works drive in a Peugeot 309, finishing ninth overall and as the leading two-wheel-drive car at the 1990 Monte Carlo. He also took part in the 1990 Paris–Tripoli–Dakar rally raid in a support role.
Ford hired Delecour to contest the 1991 World Championship in a four-wheel-drive Sierra Cosworth. At the Monte Carlo he took the lead from reigning champion Carlos Sainz before losing five minutes to a suspension failure on the final night, dropping to third. He ended 1991 seventh in the championship and returned for 1992, finishing sixth, with second places on the Tour de Corse and other events.
The 1993 season saw Delecour finally assert himself as a genuine title contender. The Ford Escort RS Cosworth replaced the Sierra, and Delecour immediately led the Monte Carlo until a final-night charge by Didier Auriol denied him the win. He rebounded by winning the Portuguese Rally and the Tour de Corse, assuming the championship lead. However, retirements in Greece and San Remo handed the title to Juha Kankkunen. Delecour still won the Catalunya Rally and finished second in the championship; his co-driver Daniel Grataloup was awarded the co-driver's championship that year.
Going into 1994, Delecour was widely considered the strongest world title contender. He won the Monte Carlo Rally — the event where his talent had always burned brightest — but then suffered an engine failure in Portugal. A road accident the following month, in which his Ferrari F40 was hit by an amateur rally driver, left him with severe leg injuries and forced him to miss four championship rounds. He returned in Finland and finished fourth but could not challenge for the title.
When the official Ford team closed at the end of 1994, its operations transferred to the Belgian concern RAS Sport. Delecour remained as lead driver alongside Bruno Thiry, but the Escort was less competitive and he did not win an event, though he finished second at Monte Carlo and Corsica in 1995. His final appearance for Ford came in Sweden in 1996.
After leaving Ford, Delecour headed Peugeot's French Rally Championship campaign in the 306 kit car, finishing third in the championship in both 1996 and 1997. He also contested selected asphalt rounds of the WRC, where the Peugeot was competitive enough to challenge for victory, finishing fourth at both the 1996 and 1997 Tour de Corse. He was involved in the early development of the Peugeot 206 WRC project and returned to the full WRC calendar for 1999, scoring consistent top-ten results including second places in Corsica and San Remo.
Delecour joined M-Sport's Ford operation for 2001 in a third, differently liveried Focus RS WRC 01. Despite being a regular scorer, his final WRC outing in Australia was marred by a heavy crash that severely injured co-driver Daniel Grataloup. He switched to Mitsubishi for 2002, partnering Alister McRae, but the Japanese manufacturer's competitiveness continued to decline. A further serious crash at Rally Australia 2002 again injured Grataloup, effectively ending the co-driver's top-line career. When Mitsubishi announced a sabbatical from the WRC after 2002, Delecour's premier-class career came to a close.
Delecour remained active in motorsport after his WRC career, contesting rally raids with an SMG V8 buggy and circuit racing with a Porsche 996 GT3 RS. In 2011, for the centenary Monte Carlo Rally, he returned in a Peugeot 207 Super 2000 and finished fifth. A further WRC comeback followed at the 2012 Monte Carlo in a Fiesta WRC, where he finished sixth and posted several top-three stage times.
He went on to compete extensively in the Romanian Rally Championship, winning the title in 2012, 2013, and 2014, and returned to the FIA R-GT Cup in 2015 driving a Porsche 911 run by Tuthill, winning the Tour de Corse round and securing the R-GT championship that year. In 2023, Delecour entered the Monte Carlo WRC round in a privately entered Rally2 Skoda, finishing tenth in class.
Delecour's career is one of the great what-ifs of WRC history. His raw pace — particularly on the asphalt stages of Monte Carlo and Corsica — was among the finest of his generation, but injuries and mechanical failures repeatedly denied him the world championship his talent deserved. The 1993 and 1994 seasons in particular, where a title victory seemed within his grasp, remain the defining chapters of a career that combined brilliance and bad luck in equal measure.