Running to become prime minister of France without ever declaring oneself to be a candidate is one of the most delicate of political arts. Jacques Chaban-Delmas, 71, a Gaullist party baron and World War II resistance hero, is proving himself to be a master practitioner.

Speculation that the longtime mayor of Bordeaux could become prime minister for the second time has focused national and international attention on what would otherwise be a humdrum election campaign in the French wine capital. It also has illustrated the room for political maneuvering still enjoyed by Socialist President Francois Mitterrand despite widespread predictions of a right-wing victory in the March 16 election.

The Fifth Republic constitution gives the president alone the right to nominate a prime minister, while reserving to parliament the power to overturn his decision. With scarcely anyone now doubting that the Socialists are about to lose their majority in the National Assembly, interest has centered on which of his political opponents Mitterrand will pick to be prime minister.

Apart from Chaban-Delmas, other runners in the prime ministerial race include the neo-Gaullist leader, Jacques Chirac, 53; former president Valery Giscard d'Estaing, 59; and Simone Veil, 58, the first female president of the European Parliament.

As the leader of the party that is likely to emerge as the dominant right-wing force after the elections, Chirac is generally considered to be the front-runner, with the mayor of Bordeaux in second place.

It is generally accepted here that the way in which Mitterrand chooses to play his trump card could determine the course of French politics until 1988, the scheduled date for presidential elections.

As an undeclared candidate for prime minister, "Chaban" (the mayor's wartime code name) spends much of his time telling journalists that he is not particularly interested in the job. The denials are always carefully hedged to make clear that, if called upon to serve France again, he would be ready.

"Becoming prime minister again is Chaban's sole raison d'etre as a politician," claimed Michel Sainte-Marie, an outgoing Socialist deputy from the Gironde district around Bordeaux. A local journalist said Chaban is looking for ways of keeping himself "politically alive" after 40 years as mayor.

The speculation about Chaban as a future prime minister stems in part from his long friendship with Mitterrand, which goes back to the resistance to Nazi occupation during the war. After the war, both men served as ministers in a succession of revolving-door governments that marked the French Fourth Republic. Chaban is one of the few French politicians to use the familiar second-person singular, or tu form of address, in talking to the patrician 69-year-old president.

The competing ambitions of the different right-wing leaders quietly have been encouraged by Mitterrand, who has refused to say whom he will name prime minister. Mitterrand knows that the left stands to benefit from the right's divisions and petty rivalries.

Aware of Mitterrand's tactics, the opposition leaders have sought to avoid being drawn into what Chirac has described as a "futile" constitutional debate. But the issue has had a tendency to pop up unexpectedly, as it did last week, when Chaban was quoted by a Swiss newspaper as saying that he was "ready" to serve as "Mitterrand's prime minister."

The Chaban public relations machine promptly swung into action, insisting that the mayor had been misquoted. A string of interviews followed in which he explained that, if the right won the election, Mitterrand would no longer be able to talk about "his" prime minister. But he also insisted on the president's constitutional prerogative of naming a premier -- a subtle way of signaling that the choice need not necessarily fall on his right-wing rival, Chirac.

According to his political associates, Chaban never has forgiven his younger Gaullist colleague for failing to support his presidential campaign in 1974. The two men represent opposite wings of the Gaullist movement. Chirac has long been allergic to reformist ideas, preferring to stress his competence as a manager of the economy. Chaban, by contrast, launched the idea of the "new society" when he was prime minister in the early 1970s, presenting himself as a kind of French John F. Kennedy.

Both Chirac and Chaban are agreed that a right-wing victory in the election inevitably must result in the transfer of executive authority from the president to a government answerable to the National Assembly. This would mark a sharp break with the Fifth Republic tradition, established by Charles de Gaulle in 1958, of an all-powerful president dominating both the government and the assembly.

In the opinion of the right-wing leaders, the key passage in the Fifth Republic constitution is Article 20, which states: "The government decides and directs the policy of the nation. It has at its disposal the administration and the armed forces."

Up until now, this clause never has been applied. By commanding the loyalty of a majority of deputies in the assembly, the president always has been in a position where he could also control the government.

Chaban now claims that de Gaulle wanted the constitution to be "elastic," permitting either a "presidential" or a "parliamentary" system of government.

The Chirac camp has gone considerably further than Chaban in attempting to limit Mitterrand's freedom of choice in naming a prime minister. The president, Chirac's associates have argued, is under an obligation to turn first to the natural leader of the new majority in the assembly. Any other nomination, they have hinted, would risk being rejected.

Flying back to Paris in his private jet after a hectic day of campaigning, Chirac was asked whether he agrees that Mitterrand is free to appoint a prime minister of his choice.

"The president has the right to ask my concierge to be prime minister, but that does not mean we would have to accept the decision," he replied wearily.

Chirac's answer underlines the power of the National Assembly to refuse a vote of confidence in a new prime minister and government. In practice, however, it could be difficult for the present opposition to reject the nomination of someone like Chaban, Giscard or Veil.

As the campaign enters its final stretch, Chaban is privately telling visitors that events during the past few months have moved in favor of Chirac's nomination. In his analysis, Mitterrand is preparing for a "rough cohabitation," which will involve a trial of strength over the precise limits of presidential powers. Under these conditions, Chaban reasons, the president would probably prefer to have an active political opponent as prime minister rather than a respected elder statesman.

In the meantime, the mayor of Bordeaux does not want to rule himself out as a prime ministerial candidate. While loyally supporting the right-wing opposition, he has conducted an intensely personal campaign in his home region. As if to prove that he still has a political future, he has chosen the word espoir (hope) as his personal slogan, splashed across the picture of a fluttering white dove.

"I can count on you and you can count on me," he tells his cheering supporters, using words as deliberately ambiguous as his campaign to become the first prime minister of the "cohabitation."