Arnoux enrolled at the Winfield Racing School in 1973 and graduated as the top student, earning the prestigious Volant Shell Competition Scholarship, which provided a free Formule Renault season. He moved into Formula Two in 1974 with Elf backing, debuting at Nogaro in fourth place. After winning the Formule Super Renault title in 1975, he returned to Formula Two with a works Martini-Renault, winning three races in 1976 and narrowly missing the championship. In 1977 he claimed the European Formula Two Championship outright, beating Eddie Cheever by twelve points after victories at Silverstone, Hockenheim, Pau, and Nogaro.
Arnoux followed the Martini team into Formula One in 1978, but the underfunded operation withdrew during the season after failing to demonstrate competitiveness. His best finishes were two ninth places. He transferred to Surtees for the final two rounds and placed ninth on his debut at Watkins Glen, but Surtees was itself on the verge of collapse. Despite their interest in retaining him, Arnoux secured a seat at the Renault factory team for 1979.
Arnoux spent four seasons at Renault from 1979 to 1982. His most celebrated moment in that period came at the 1979 French Grand Prix at Dijon-Prenois, where his fierce wheel-to-wheel battle with Gilles Villeneuve's Ferrari over second place — complete with repeated contact at racing speed — became one of the most replayed sequences in the sport's history.
In 1980, Arnoux scored his first two Formula One victories in consecutive races: at Interlagos in Brazil and at the high-altitude Kyalami circuit in South Africa, where the turbocharged Renault RE20's power advantage over the Cosworth-engined field was pronounced. He led the World Championship briefly before engine unreliability undermined his season.
Tension with incoming teammate Alain Prost escalated through 1981 and 1982. At the 1982 French Grand Prix at Paul Ricard, Arnoux crossed the line ahead of Prost for Renault's first one-two finish despite an alleged pre-race team-orders agreement that Prost should win. Arnoux denied any firm instruction had been given. He took one further win that year at Monza and was released by Renault at season's end as the partnership with Prost had become untenable.
Arnoux joined Ferrari in 1983 alongside Patrick Tambay. The combination proved popular with the Tifosi, as both drivers attacked hard and generated strong results. Arnoux won three Grands Prix that year — at Montreal, Hockenheim, and Zandvoort — and was a genuine title contender entering the final round, the South African Grand Prix. Engine failure there ended his bid; he finished third in the championship behind Nelson Piquet and Prost. The pair's combined results also delivered Ferrari the 1983 Constructors' Championship.
The Zandvoort win proved to be the last of his Formula One career. A less successful 1984 followed as Michele Alboreto took the initiative at Maranello and Arnoux appeared to lose motivation. He left Ferrari by mutual consent after the opening race of 1985.
After a gap from racing, Arnoux joined the French Ligier team in 1986, competing with turbocharged Renault engines. The cars proved uncompetitive on Pirelli tyres and results were poor. For 1987, Ligier had arranged exclusive use of a new Alfa Romeo four-cylinder turbo engine, but Arnoux's dismissive pre-season comparison of the unit to "used food" prompted Fiat — Alfa's parent — to withdraw the project. The team ran Megatron engines instead, and Arnoux's sole point of the year came with sixth at Spa.
The 1988 and 1989 seasons with the naturally aspirated Ligier JS31 and JS33 were difficult. Arnoux failed to qualify on multiple occasions and drew persistent criticism for not using his mirrors when being lapped. His final championship points came from fifth place at the 1989 Canadian Grand Prix. He retired from the sport after the rain-soaked 1989 Australian Grand Prix in Adelaide, where his Ligier was punted into retirement by Eddie Cheever's Arrows.
Arnoux finished his Formula One career with 181 World Championship points, seven wins, twelve fastest laps, and twenty-two podiums in 149 starts. His eighteen pole positions underscore a raw pace that was occasionally overshadowed by controversy. He is best remembered for the Dijon battle with Villeneuve in 1979 — a spontaneous, unscripted display of racing at its most vivid — and for the team-orders defiance at Ricard in 1982 that crystallised the combustible dynamics of the Prost-Arnoux era at Renault. After retiring he established an indoor karting business in France and regularly appeared at historic events on behalf of Renault.