Delecour began rallying in 1981 in the French national championship. He entered his first major international event, the Monte Carlo Rally, three years later in a Talbot Samba. For 1985 and 1986 he drove in the Peugeot 205 Cup, finishing third in both seasons, earning him a degree of works support from Peugeot. That support grew into a full works drive in a Peugeot 309 in 1989 and 1990, in which latter year he finished ninth overall and as the first two-wheel-drive car at Monte Carlo.
Delecour joined Ford for the 1991 World Championship. Although the four-wheel-drive Ford Sierra Cosworth was not fully competitive, Delecour displayed remarkable pace at Monte Carlo, taking the lead from reigning world champion Carlos Sainz on the third day before suspension failure on the final night dropped him to third. He ended 1991 seventh in the championship. Results improved in 1992 with the continued use of the Sierra, as Delecour took second on the Tour de Corse and third on the San Remo Rally.
For 1993, the Sierra was replaced by the Ford Escort RS Cosworth. Delecour led the Monte Carlo on the final night until Didier Auriol charged past, leaving him second. He then won the Portuguese Rally and Tour de Corse in succession to lead the championship. Retirements in Greece and San Remo handed the title to Juha Kankkunen, but Delecour won again in Catalunya and finished second in the championship. His co-driver Daniel Grataloup was awarded the co-driver's title that year.
Delecour was widely regarded as the strongest title contender for 1994 and he duly won the Monte Carlo Rally. Engine failure in Portugal then interrupted his campaign. A road accident shortly afterward — in which the Ferrari F40 he was driving was struck by an amateur rally driver practicing for a local event — left him with severe leg injuries and forced him to miss four championship rounds. He returned in Finland but could not recover the title.
The official Ford team was wound down at the end of 1994, replaced by Belgian concern RAS Sport. Delecour remained as lead driver but the Escort RS Cosworth was less competitive. He took second at Monte Carlo and Corsica in 1995 before his final Ford outing in Sweden 1996.
Peugeot then engaged him to lead their French Rally Championship campaign in the 306 kit-car, in which he finished third in both 1996 and 1997 while winning several events outright. He also contested selected WRC asphalt rounds, finishing fourth at the Tour de Corse in both those years. He was subsequently involved in the early development of the Peugeot 206 WRC, returning to the full WRC programme in 1999. He did not win events that year but scored consistent top-ten finishes, including second in Corsica and San Remo, the latter overshadowed by conflict with teammate Gilles Panizzi, who won the event.
Delecour moved to Ford again in 2001, driving an M-Sport Focus RS WRC, but a heavy accident in Australia involving co-driver Daniel Grataloup clouded the season. He switched to Mitsubishi for 2002, replacing both outgoing four-time world champion Tommi Mäkinen and Freddy Loix alongside Alister McRae. Mitsubishi's competitiveness continued to decline during that period, and Delecour suffered another heavy accident at Rally Australia 2002 that effectively ended Grataloup's top-line career. When Mitsubishi announced a sabbatical from WRC through 2004, Delecour's world championship career came to a close.
In 2011, marking the 100th anniversary of the Monte Carlo Rally, Delecour returned to competition in a Peugeot 207 Super 2000, finishing fifth. He competed at the 2012 Monte Carlo Rally in a Fiesta WRC, finishing sixth and setting several top-three stage times. Through 2012 and 2013 he competed in the Romanian Rally Championship, winning the title three times and competing in selected IRC events.
In 2014 and 2015 he contested the FIA R-GT Cup for GT cars in rallying, driving a Porsche 911 prepared by Tuthill. He won class at Monte Carlo and outright at the Tour de Corse in 2015, securing the FIA R-GT championship title.
In 2023, Delecour entered the Monte Carlo WRC round in a privately entered Rally 2 Skoda, finishing tenth in his category — a final demonstration of his enduring enthusiasm for the sport.
Delecour's career is defined by brilliance and misfortune in roughly equal measure. His pace on asphalt rallies was considered among the finest of his generation, and his 1993 championship challenge — in which he led the series before a run of retirements — remains one of the great near-misses in WRC history. His 1994 Monte Carlo victory and his later revival in the R-GT Cup underline a career built on genuine speed rather than results alone.