As his foes to the right continued to fight among themselves, French President-elect Francois Mitterrand today began working on his new government and on the Socialist Party's campaign for parliamentary elections, in which it hopes to defeat the center-right majority. p

The party announced that Mitterrand would make no statements until he takes office on May 25. Until then, the party said, defeated President Valery Giscard d'Estaing and Prime Minister Raymond Barre will continue to be responsible for the conduct of affairs of state.

A traditional team of five persons headed by Mitterrand lieutenant Pierre Beregovoy, a hardened veteran of Socialist negotiations with the Communist Party, was set up at Socialist Party headquarters to deal with the Giscard government. The limited size of the team seemed intended to underline Mitterrand's determination to keep Giscard at arm's length and to hold him responsible for everything the government does until the transfer of power in two weeks.

Frequent visitors to Mitterrand's home during the past two days have included university economist Jacques Delors, once an aide to National Assembly president and 1974 Gaullist presidential candidate Jacques Chaban-Delmas; Mayor Pierre Mauroy of Lille, favored to become prime minister; Claude Cheysson, the French member of the European Common Market Executive Commission and the leading candidate for foreign minister; Mayor Charles Hernu of the Lyons suburb of Villeurbane and virtually the party's shadow defense minister; Mayor Gaston Defferre of Marseilles, the grand old man of the moderate wing; and Michael Rocard, Mitterrand's unsuccessful right-wing challenger for the Socialist presidential nomination.

There were also visitors from the party's left wing, such as Pierre Joxe and Jean-Pierre Chevenement, and from Mitterrand's personal pack of young wolves, such as Jacques Attali and Laurent Fabius. But the dominant tone of the transition has been the established party moderates, who have been acting as spokesmen and who seem to be tipped for the key jobs.

However, it seems unlikely that the secretive Mitterrand has discussed who will get what position even with his closest friends. When the president-elect went for a walk today, he responded to a question by smilingly placing his finger over his closed lips.

The speculatin about Mauroy as prime minister is based on his effective television performances on behalf of Mitterrand during the campaign, his reassuring image, his demonstrated political ability, the way in which he neutralizes the party's right wing and his team of what is generally viewed as France's best political technicians.

Such political savvy may be the only factor that places Mauroy's appointment to the prime ministership in doubt. Winning the legislative elections -- which Mitterrand plans to schedule for late June -- is considered the new government's first priority. Mauroy might be considered far more valuable at the Interior Ministry, which organizes elections and centralizes the government's political intelligence-gathering.

Socialists are counting on a bandwagon effect to make them the dominant group in the National Assembly. The party now has 117 members of the 491-seat body. The Communists have 86. The Gaullists and Giscardists split the rest of the Assembly almost evenly.

The Socialists could both take over many of the Communist seats and wrest some from the bitterly divided Giscardist party, the Union for French Democracy, if they receive a few more strategically placed votes than they did in the presidential elections.

A meeting of the Giscardist parliamentary group today was marked by screaming matches and personal recriminations the likes of which veteran parliamentary observers said they had never seen.

Mitterrand aide Laurent Fabius said the Assembly's divided center-right majority was "giving us a beautiful gift."

A statement last night by Giscard that his defeat came because of "premeditated treason" complicated attempts top renew an electoral alliance with Gaullist Party leader Jacques Chirac, considered the key to maintaining a strong center-right group in the Assembly.

Meanwhile, Mauroy let it be known that he has initiated contact to discuss electoral strategy, not only with the Communists, but also with a broad range of center-left-wing Gaullists who came out for Mitterrand in the presidential runoff.