France's new conservative prime minister, Jacques Chirac, got an early start in politics by hawking the Communist Party newspaper on street corners and signing a petition against nuclear weapons.

Among his other distinctive qualities: he is the only former prime minister under the 28-year-old Fifth Republic to have quit in protest because of differences with the president. And he is almost certainly the only French prime minister to have worked once as a soda jerk at an all-American Howard Johnson's.

These days, there are few French people who would accuse Chirac, the mayor of Paris, of harboring leftist sympathies. As the leader of the neo-Gaullist Rally for the Republic, Chirac played a prominent role in the recent election campaign, vigorously denouncing five years of Socialist rule before appreciative audiences of right-wing supporters.

An energetic politician who served as prime minister from 1974 to 1976 under president Valery Giscard d'Estaing, Chirac was the natural choice of the right-wing majority in the National Assembly to head the new government. Many political observers here believe that he would like to use the post as a stepping stone to becoming the official right-wing candidate in the next presidential elections, scheduled for 1988.

Chirac, 53, has promised to chart a new economic course for France, professing admiration for the free-market philosophy of the Reagan administration. But his narrow, three-seat majority in the new National Assembly could pose obstacles to the speedy implementation of election campaign promises. Two of those pledges are to return important sectors of French industry to private ownership and reduce state controls over the economy.

As prime minister, Chirac will be obliged to work closely with Socialist President Francois Mitterrand. Such a division of power between political opponents is without precedent in the history of the Fifth Republic, established by Gen. Charles de Gaulle in 1958, and there is some confusion here about how, or even whether, it will work.

In many ways, Chirac is Mitterrand's opposite, quite apart from their political differences. While the president is known as "the Florentine" because of his reputation for Machiavellian intrigue, Chirac acquired the nickname of "the Bulldozer" because of the enthusiastic way in which he set about fulfilling the orders of former prime minister Georges Pompidou, his political mentor.

"If I asked Chirac to dig a tunnel in the night between my home and Matignon the prime minister's office , he would do it and only ask me why the following morning," Pompidou once remarked.

In contrast to Mitterrand, who has highbrow literary tastes, Chirac joked this week that the only books he had read in the past few months were an airline timetable and a Michelin guide. In fact, his cultural interests are eclectic, ranging from detective novels and racy American adventure movies to Kandinsky paintings and Chinese history. Unlike the president, who seems to take pride in knowing no foreign language, Chirac speaks fluent, if heavily accented, English.

Chirac's knowledge of America goes back to his student days, when he spent a summer studying at Harvard. At one point, he considered marrying the daughter of a prosperous South Carolina cotton farmer. His admiration for the United States survived a tussle with the Immigration and Naturalization Service, which twice delayed giving him a visa because of his brief flirtation with communism and pacifism in 1950.

Looking back at this period in a recent interview with the Paris daily Le Monde, Chirac explained that many French young people saw the Communist Party as the logical alternative to the extreme right.

Chirac's prodigious energy -- he put in 18-hour days during the campaign and traveled more than 50,000 miles -- has won him both admirers and enemies. To his supporters, he is a strong leader who can get things done. To his opponents, he is a somewhat frightening, authoritarian figure. In private, however, he is charming and solicitous, the reverse of his public image.

In a portrait of the neo-Gaullist leader written in 1975, Mitterrand noted that the words Chirac and action seemed to go together. The future Socialist president wrote of his future conservative prime minister: "Intelligent, quick, he runs rather than walks. You can't imagine this man as an insomniac. What a stomach! He doesn't eat, he devours, and what he consumes, he burns off, keeping himself from becoming fat by constantly moving forward."

Mitterrand commented some years later about Chirac's lackluster speaking style: "He talks like a typewriter."

Like many prominent French politicians, on both left and right, Chirac was trained as a high state bureaucrat at the elite Ecole Nationale d'Administration. After serving in Pompidou's private office in the early 1960s, he went on to become a junior minister in charge of employment, Giscard's deputy at the Ministry of Finance and minister of the interior.

Chirac became prime minister in 1974 under Giscard, who was elected president following Pompidou's death. The two men quickly quarreled over how the government should be run, with Chirac expressing serious reservations about a gradual program of reforms supported by Giscard. The conflict ended with Chirac's resignation in 1976.

The mayor of Paris again angered Giscard in 1981 by failing to swing Gaullist support behind the head of state in the second round of the presidential election. It took Giscard several years to make up with Chirac, whom he largely blamed for his defeat. Today, relations between the two men are correct, although scarcely cordial, based on their mutual interest in demonstrating right-wing unity against the left.

If Mitterrand and Chirac fall out, as seems quite possible, the outcome will be much less clear. Unlike previous Fifth Republic prime ministers, Chirac does not owe his position to the president but to his control over a majority of deputies in the National Assembly. He has made clear that he does not consider that Mitterrand has the right to fire him without calling fresh elections to the assembly.

On foreign policy, Chirac expressed complete support for Mitterrand's decision to endorse the deployment of U.S. medium-range missiles in Western Europe in 1983, widely seen as a break with the traditional Gaullist policy of maintaining an aloof equidistance between the two superpowers. But he has criticized the president for ruling out official French participation in Reagan's Strategic Defense Initiative.

Insisting that it was impossible to stop the new technology, Chirac told an interviewer earlier this month: "If France does not associate with its European partners, in cooperation with its American allies, it will find itself left on the wayside, becoming an underdeveloped country in less than 50 years."