Giroix entered motorsport through French Formula Renault in 1984, finishing fourth in the championship. He moved to the French Formula Three Championship in 1985, finishing twelfth, then made limited appearances in the British and German Formula 3 series in 1986. In 1987 he contested two prestige Formula 3 rounds — Monaco and Macau — alongside making his debut in the World Touring Car Championship and his first DTM start, driving an Alpina BMW M3.
In 1988 Giroix joined Sport Auto Racing for the first five rounds of the International Formula 3000 season. He started from the front row on debut at Circuito de Jerez, qualifying second and finishing fourth, which placed him seventeenth in the championship on the strength of that single points finish.
Giroix committed fully to the DTM in 1989, joining the respected Schnitzer Motorsport squad with a BMW M3. He was highly competitive, recording ten podium finishes across twenty-one starts and finishing third in the overall points standings. That same year he entered the 24 Hours of Nürburgring alongside Emanuele Pirro and Roberto Ravaglia, and the Team Bigazzi BMW M3 crew won the race outright.
In 1990 Giroix remained with Schnitzer but dropped to ninth in the championship. He compensated with a significant endurance victory, winning the Spa 24 Hours together with teammates Johnny Cecotto and Markus Oestreich. His DTM involvement wound down after 1991, when he made ten starts for Zakspeed in a Mercedes-Benz 190E 2.5-16 Evolution II, finishing twenty-third in points.
Between 1992 and 1994 Giroix raced in the French Supertouring Championship. He drove a BMW M3 for Garage du BAC in 1992, finishing fourth in points. In 1993 he secured a factory drive with SEAT, contesting seven rounds in a Toledo and finishing sixteenth in points. That year he also took third place in the Porsche Carrera Cup France. He returned to SEAT full-time in 1994, finishing eleventh in French Supertouring while placing sixth in the French Carrera Cup.
In 1995 Giroix elevated his program substantially, establishing his own Giroix Racing Team to campaign a McLaren F1 GTR in the BPR Global GT Series. He achieved two podium finishes from five starts and made his 24 Hours of Le Mans debut that year. The 1995 race was dominated by GT1-class McLaren F1 GTRs and the Giroix car finished fifth overall and fourth in class.
In 1996 Giroix split his BPR campaign between his own McLaren F1 GTR and a factory Lotus Esprit. The Giroix McLaren did not finish at Le Mans that year. For 1997 his team took on the role of factory-backed outfit for the Lotus Elise GT1 in the FIA GT Championship, though the season proved unsuccessful. Giroix made only a single FIA GT start in 1998, driving a Zakspeed Porsche 911.
Giroix remained active in sports car racing through much of the 2000s. He resurfaced competitively in the Speedcar Series in 2008, contesting all eight rounds and finishing tenth in the final standings. As of 2010 he continued to race, making four starts in a Lamborghini Gallardo in the French GT Championship.
Giroix is remembered for his strong 1989 DTM campaign with Schnitzer Motorsport and for the team victories at the Nürburgring 24 Hours and Spa 24 Hours. As a privateer entrant his McLaren F1 GTR program at Le Mans represented the boldest chapter of his career, placing him among the independent operators who made the mid-1990s GT era particularly rich.
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