Dreyfus was born and raised in Nice to a Jewish family. He showed an early interest in automobiles, learning to drive before the age of nine. Through his brother Maurice, who later became his manager, he joined the Moto Club de Nice. In 1924 he won his class in the first amateur race he entered and went on to win three consecutive French Riviera championships over the following five years.
In 1929 he entered his first professional race, the inaugural Grand Prix of Monaco, finishing first in his class and fifth overall. The Monaco result set the stage for what followed the next year.
In 1930, Dreyfus won the Monaco Grand Prix outright in a Bugatti, beating the highly regarded Bugatti factory team — led by the previous year's winner William Grover-Williams — and the local favourite Louis Chiron by 22 seconds. His winning strategy was unconventional: calculating that factory cars would always have a pace advantage over his privately entered machine, he had additional fuel tanks fitted to his Bugatti so he could run the entire race without a pit stop. The gamble worked.
The subsequent years tested Dreyfus differently. Germany's government poured essentially unlimited resources into the Mercedes-Benz and Auto Union racing programmes, producing the dominant Silver Arrows that swept most of the major Grands Prix of the mid-1930s. Where many leading European drivers — Chiron, Achille Varzi, Tazio Nuvolari, Richard Seaman — accepted contracts with the German teams, Dreyfus, as a Jewish driver, had no such option. He competed instead with French machinery, often outgunned on paper and required to win through strategy and daring.
In 1937 the French government announced the Prix du Million — a one-million-franc prize for any French car that could beat the German teams in a timed trial at the Autodrome de Montlhéry. Dreyfus drove a Delahaye 145 for the Écurie Bleue team of patron Lucy O'Reilly Schell, pushing the car's Dunlop tyres to the fabric in his effort to beat first all other competitors and then, in the final run, the Bugatti team. He won the prize for Delahaye.
The 1938 Pau Grand Prix became Dreyfus's most celebrated achievement against the German teams. Two new Mercedes-Benz W154 Silver Arrows appeared at the tight street circuit in southern France. One crashed in practice. The legendary Rudolf Caracciola, forced to make a pit stop and relieved by Hermann Lang, could not respond to Dreyfus's strategy. Dreyfus drove the Million Franc Delahaye non-stop through the entire race to win, defeating the Mercedes works team and becoming a national hero in France.
When the Second World War began in September 1939, Dreyfus joined the French Army as a truck driver. In 1940 he was dispatched to the United States to drive a Maserati in the Indianapolis 500 alongside fellow Frenchman René Le Bègue. Neither driver spoke English, and unfamiliarity with American race rules compounded their difficulties; the pair co-drove the one car they qualified from the back of the grid to tenth place.
With the German occupation of France and his profile as a Jew who had publicly humiliated the German racing effort, Dreyfus was advised not to return to occupied France. He settled in New York City, where he opened a French restaurant called Le Gourmet. After the United States entered the war in 1942 he enlisted in the US Army and served in Europe as an interrogator in the Italian Campaign. He became an American citizen in 1945.
After the war he and his brother Maurice opened another French restaurant in New York, Le Chanteclair, which became an informal meeting point for the international racing community and eventually evolved into the Madison Avenue Sports Car Driving and Chowder Society, meeting monthly from its founding in March 1957.
He continued to race sporadically after the war, including at the 1952 24 Hours of Le Mans, and his last race was the 1955 12 Hours of Sebring, where he captained the Arnolt-Bristol Racing Team to the Sebring Team Trophy and a 1-2-3 class finish.
Dreyfus was invited to Monaco in 1980 to celebrate the 50th anniversary of his 1930 victory, driving throughout Europe on a tour of his racing career's significant sites. At the anniversary banquet he sat once again in the original Bugatti. He also served as Grand Marshal of the 1980 United States Grand Prix at Watkins Glen. He died on 16 August 1993. His career stands as one of the defining stories of interwar motor racing: a driver who refused the dominant team, competed for his country with inferior cars, and won the races that mattered most.