Muller comes from a motorsport family that has produced multiple generations of professional drivers. Her younger brother Yvan Muller went on to win four World Touring Car Championship titles, while her son Yann Ehrlacher has competed at the highest level of touring car racing. Cathy Muller was among the earliest members of the family to pursue professional racing.
Muller began her racing career in the Renault 5 Turbo series in the early 1980s, one of the most competitive grassroots championships in France at the time. She graduated from there into the French Formula Renault Turbo Championship, finishing fifth driving a Martini Mk36.
Her single-seater career continued with a move into European Formula 3, where she drove for David Price Racing in 1983 and Pavesi Racing in 1984. In 1985, she competed in the British Formula Three Championship with David Price Racing, finishing ninth in the standings. She later returned to the French Formula Three Championship, finishing tenth.
Muller first raced in Formula 3000 in 1986, qualifying for four events during the season. She returned to the series in 1988, though she failed to qualify for the season-opening race. Formula 3000 was the primary feeder series for Formula 1 during this era, and Muller's participation placed her among a small number of women who reached that level of open-wheel competition in Europe.
In 1989 she made a single appearance in American Indy Lights racing before making a fuller commitment to the series in 1990, finishing sixteenth in the championship standings.
Muller made her debut in the World Sportscar Championship at the 1984 Sandown 1000, driving for Gebhardt Motorsport. In 1987, she achieved a seventh-place finish in the 1000 km of Nürburgring. Her sportscar programme reached its peak when she entered the 1991 24 Hours of Le Mans, one of the most prestigious endurance events in motorsport, though she did not finish the race.
In 1993 and 1994, Muller competed in the Peugeot 905 Spider Cup, a one-make series using the iconic Peugeot 905 sportscars that had recently triumphed at Le Mans. She finished fifth in the championship in 1993 and improved to second place in 1994, capping her career with her strongest results in a single-marque series.
Cathy Muller's career spanned more than a decade and an unusually diverse range of motorsport disciplines, from French domestic circuits to the World Sportscar Championship and the famous Circuit de la Sarthe. As one of the few women to compete in Formula 3000 during the 1980s, she helped define what was possible for female drivers in top-level European single-seater racing. Her family's continued presence in professional motorsport through Yvan Muller and Yann Ehrlacher makes the Muller-Ehrlacher lineage one of the most remarkable in French motor racing history.