The France Socialist leader, Francois Mitterrand, won the presidency of France today, defeating the center-right coalition that has ruled France for 23 years.

Nearly complete returns gave Mitterrand 52.1 percent of the runoff vote against incumbent President Valery Giscard d'Estaing, a substantially broader margin than the 50.8 percent that Giscard tallied in 1974 to defeat Mitterrand. The Socialist won a 1.2 million-vote advantage over Giscard this time, compared with the 425,000 votes by which Giscard won his seven-year term in 1974.

With 98 percent of the votes counted tonight, Mitterrand had 15.6 million and Giscard 14.4 million.

Mitterrand's victory opened the way for legislative elections he has pledged to call within two months to seek a parliamentary majority in accord with his socialist principles. If his victory in the presidential election is backed up in the legislative voting, it will upset the delicate balance between conservative and socialist-oriented governments within Western Europe's 10-nation Common Market. If it is rejected -- bringing back a majority hostile to his program -- the stage will be set for a severe test of the Fifth Republic institutions tailor-made for the unusual dimensions of Gen. Charles de Gaulle in 1958.

A leftist who is on the record as favoring nationalization of key French private industries, Mitterrand nevertheless is a firm supporter of Western defense efforts and favors an even firmer stand against the Soviet Union than Giscard, who has been accused by many moderates of being too accomodating to Moscow.

French state television said tonight that every major Western leader except President Reagan had sent Mitterrand a congratulatory telegram.

[But in Washington, an assistant White House press secretary said late Sunday night "I can confirm that the president has sent a congratulatory message to Mr. Mitterand." The White House declined to release the text of the message, but the spokesman said it was transmitted in "late afternoon or early evening."]

The vote seemed to show that the French electorate is no longer afraid that a now-weakened Communist Party can impose its will on Mitterrand. Giscard's appeal to that fear was considered the major factor in the defeat of the left in national legislative elections that it had generally been expected to win three years ago.

Intense squabbling between Communists and Socialists since then has underlined for moderate voters that Mitterrand is no longer allied to the Communists. Those disputes made it difficult for Giscard to use the same argument convincingly this time.

The incumbent president's own personal image -- originally that of a fresh, forward-looking liberal -- was tarnished by his government's failure to deal adequately with mounting unemployment and by a number of accusations of scandals, some of which touched him personally.

Mitterrand waged a low-profile campaign designed to reassure voters that there would be no social upheavals under his rule. He apparently managed to persuade the voters that his program of nationalizing 11 industries -- including insurance, armaments, pharmaceuticals and chemicals -- is moderate in a country where a large part of industry was nationalized after World War II.

Mitterrand's victory was a major personal vindication for the 64-year-old veteran politician, who was running for president for the third and clearly final time. His first attempt was in 1965 against De Gaulle, a national hero and then the incumbent president.

Mitterrand surprised the French political world in that race by forcing De Gaulle into a runoff, denying him an outright majority in the first round of voting. Mitterrand wound up with 45 percent of the vote in that runoff but since then he has been widely accused of being an old face who had for too long blocked the rise of fresh figures who could bring the left to victory.

In a telegram to Mitterrand tonight, Giscard, 55, conceded within minutes after the first results were announced. The new president-elect later publicly thanked Giscard for his good wished and added that he would need everyone's help.

"Only the entire national community can answer the demands of the present times," Mitterrand said. "I will act with resolution so that, while maintaining fidelity to my committments, it may find the path of necessary reconciliation. We have so much to do together, and so much to say, too. Hundreds of millions of men on earth will know tonight that France is ready to speak to them with words that they had come to love to hear from her."

There was an outburst of joy and chants of "victory, victory, victory," outside Socialist headquarters on the Left Bank of Paris. The party's first secretary, Lionel Jospin, called for a victory celebration at the huge Square of the Bastille, the site of the prison whose fall according to tradition signaled the start of the French Revolution.

Tens of thousands of joyous demonstrators gathered there to hear Socialist speakers led by Michel Rocard, who had unsuccessfully challenged Mitterrand for the party candidacy.

"France will choose a new path," Rocard exulted.

The prestigious Champs Elysees was the scene of wild celebrations, with cars full of youths speeding up and down the broad avenue honking their horns. Groups of youths chanted, "Giscard into the closet."

"I'll probably live to regret it, but today I'm pleased," said a Parisian moderate.

Several prominent Giscard supporters clearly indicated that they do not intend to give the new president any honeymoon period. Women's Affairs Minister Monique Pelletier, one of Giscard's leading campaign organizers, spoke of her "anguish" over the outcome and steadfastly refused in a televised debate to accept appeals by Socialist participants to be a good loser and to stop trying to frighten the voters with the Communist specter.

"All those who did not vote for Francois Mitterrand have the right to be anxious about the future of France," she said, adding that she would become a determined opponent.

Jockeying began immediately for national legislative elections. Mitterrand will have the power to dissolve the National Assembly two years before the end of its present mandate as soon as he takes office at the end of this month.

Mitterrand has indicated the elections will take place in the latter half of June.

While conceding, Giscard added in his telegram to Mitterrand, "I will, of course, continue to defend the essential interests of our country."

As a former president, Giscard is barred from seeking an assembly seat. He is automatically a member for life of the Constitutional Council that passes on the constitutionality of laws.

In his reply to Giscard, Mitterrand said, "I, address my best wishes to the man who led France for seven years. Beyond the political struggles and our disagreements it is now for history to judge each of our acts."

Gaullist leader Jacques Chirac made a statement clearly indicating his intention to replace Giscard as the leader of the defeated center-right coalition. Chirac said he would announce political initiatives in the next few days.

Communist leader Georges Marchais claimed credit for the victory because of his party's decision to support Mitterrand unconditionally in today's runoff election, between the top two candidates who emerged from a field of 10 in the first-round election April 26.

Marchais, who got 15 percent two weeks ago -- his party's poorest showing in 45 years -- said in a public message from the Communist leadership to Mitterrand that the Communists are "ready to assume our responsibilities in a government."

Computer projections indicated that 88 percent of those who had voted for Marchais had followed the party call to vote for Mitterrand in the runoff. The computer showed that about 30 percent of the Gaullist voters did not follow Chirac's deliberately lukewarm appeal to vote for Giscard. The 30 percent was split about equally between those who stayed at home and those who switched outright to Mitterrand.

Mayor Pierre Mauroy of Lille, generally considered a leading candidate to be Mitterrand's prime minister, said tonight that there was no question of bringing Communists into the transitional Cabinet that will conduct the new elections after the National Assembly is dissolved. But Mauroy said that negotiations would be held with them and others after the elections to work out a "contract" for a government program.