Artzet began his professional racing career in Formula Renault and Formula 3 in France. At the 1986 International F3 race at Monaco, he demonstrated immediate pace by qualifying on the front row of the grid in a Ralt RT30, ultimately finishing 12th in the race itself. That same year he finished third in the Formula Renault France championship, behind runaway champion Érik Comas and future Simtek driver Jean-Marc Gounon — a respectable result in a strong field.
The 1987 season brought Artzet his breakthrough result. He comprehensively won the International F3 race at Monaco, having qualified on pole position and set the fastest lap during the race — a clean sweep of all headline honours. Jean Alesi joined him on the podium, and the result announced Artzet as a driver of genuine talent among the French Formula 3 generation of that era. He finished seventh overall in the Formula 3 France series standings for 1987, and also made a single appearance in the World Touring Car Championship that year, racing a Ford Sierra for Wolf Racing.
In 1988 Artzet returned to the Monaco International F3 race once more and again secured pole position, but contact on lap 10 ended his race prematurely. Alongside the Monaco appearance, he raced six times in the Formula 3 France series, collecting two podium finishes over the course of the season.
Artzet stepped up to the International Formula 3000 series in 1988 with Team Racetech 3000, entering three race weekends but failing to qualify for two of them. He completed one race, at Zolder, qualifying 17th and finishing 14th.
A return to Formula 3000 came in 1989, again with Team Racetech 3000. Artzet qualified for the first three rounds of the season, with his best and only finish being 7th at the 1989 Rome Grand Prix held at Vallelunga. For 1990 he switched to the Apomatox 3000 team, and in his final Formula 3000 appearance at Birmingham he secured a 3rd-place podium finish — the best result of his Formula 3000 career. At the time, Rémi Decorzent, who would later become a race engineer at Toyota F1, served as the team's race engineer.
Parallel to his single-seater activities, Artzet pursued sportscar racing. In 1989 he joined Toyota Motorsport's TOM's racing division, competing in a Toyota 88C at both the Coupe de Dijon and the 24 Hours of Le Mans. He also raced in the 24 Heures de Francorchamps in a TOM's-run Toyota Supra that year.
After an absence from racing in 1991, Artzet made one further return to Le Mans in 1992, driving for Welter Racing. He qualified 27th on the grid but retired from the race without completing it.
Following his retirement from professional racing, Artzet relocated to Nouméa, New Caledonia. He continued to participate in motorsport at an amateur level, regularly racing his superbike at Eastern Creek.
Artzet's defining achievement was his dominance of the Monaco International Formula 3 event: qualifying on the front row in 1986, taking pole in 1987 and winning with pole and fastest lap, and taking pole again in 1988. His two Monaco appearances at the front of the grid bookend a career that placed him in competition alongside drivers who would go on to Formula 1 success, including Jean Alesi and Érik Comas, reflecting the quality of the French Formula 3 scene in the late 1980s.