Moll was born to a French father and a Spanish mother who had emigrated to Algeria, then a French colonial territory. He began racing in 1930, driving a Lorraine-Dietrich in sporadic local events in Algeria. His talent came to the attention of Marcel Lehoux in 1932 — a successful Grand Prix driver who ran a large trade company in Algeria. Lehoux offered Moll his Bugatti for the Grands Prix at Oran and Casablanca. In Oran, Moll led from the start before falling to second and retiring; he retired again at Casablanca. Undeterred, Lehoux brought him to France for the Marseilles Grand Prix at Miramas, where Moll finished a sensational third behind the Alfa Romeos of Raymond Sommer and Tazio Nuvolari — an extraordinary debut on an unfamiliar circuit.
In 1933, Moll continued in a Bugatti, placing second to Lehoux at Pau in a snowstorm on a track he had never seen. He then obtained an Alfa Romeo 8C-2300 using family money. Despite its inferiority to the full Alfa P3s run by the Scuderia Ferrari drivers, Moll finished third at Nimes, Miramas, Comminges, and Nice, and nearly won the Marne Grand Prix at Reims. His consistency and speed throughout the season convinced Enzo Ferrari to sign him to drive P3s for 1934.
The 1934 Grand Prix season saw the German factories — Mercedes-Benz and Auto Union — deploy their new 750-kilogram formula cars, which would come to dominate European racing. Despite this formidable new opposition, Moll's 1934 campaign for Scuderia Ferrari was exceptional.
At the Monaco Grand Prix, Moll inherited the lead when his teammate Louis Chiron, nursing a troubled P3, spun into sandbags at the Station Hairpin with fewer than two laps remaining. Moll converted the position into his first Grand Prix victory.
A month later at Tripoli, he finished a close second to teammate Achille Varzi amid accusations that Varzi had attempted to force him off the road. Moll also won the Avusrennen, where his streamlined Alfa Romeo — fitted with a 3.2-litre engine producing approximately 265 bhp — prevailed after Auto Union rookie Hans Stuck suffered clutch failure while dominating the race.
Over the rest of the season he scored additional podiums: third in the French Grand Prix at Montlhéry behind Chiron, and second at both the Targa Florio and the Coppa Ciano, trailing Varzi on each occasion.
On 15 August 1934, at the Coppa Acerbo on the Pescara Circuit in wet and windy conditions, Moll was running second and chasing Luigi Fagioli for the lead when he lost control at near-maximum speed on a narrow straightaway while passing Ernst Henne's Mercedes. His Alfa Romeo P3 went into a ditch and struck a bridge. He died from his injuries shortly thereafter. The precise cause of the accident was never determined.
Enzo Ferrari, who had seen virtually every significant Grand Prix driver of the interwar era, consistently listed Moll among the very best he had ever witnessed. He believed that, had Moll lived, he could have become one of the greatest drivers in the history of the sport. Moll was buried in the Maison Carrée Alger cemetery in Algeria. His career, spanning barely four seasons and ending at 24, remains one of the most tantalising truncated careers in the history of Grand Prix racing.