With about 2.2 million of 2.7 million votes counted, Mr. Hollande, a lawyer and career politician, was ahead of the party leader, Martine Aubry, by about 56 percent to 44 percent in their second-round contest.
Ms. Aubry conceded defeat in a televised statement, saying she wanted “to warmly salute the victory of François Hollande” and calling for party unity “around our candidate.”
The incumbent, President Nicolas Sarkozy, has yet to announce his candidacy, concentrating on his duties with the long crisis over the euro, budget deficits and the solidity of French and European banks. He is to attend a vital European Union summit meeting this month and to preside over a summit of the Group of 20 economies early next month in the southern city of Cannes. Even if he plans to seek a second five-year term — and his aides are preparing for him to do so — he may not formally announce until early next year. The first round of the presidential election is scheduled for April 22.
Mr. Sarkozy trails Mr. Hollande in opinion polls, but now that he has a specific opponent, the campaigning, overt or otherwise, will start in earnest. Other candidates are expected to run as well, including Marine Le Pen, the leader of the far-right National Front, and candidates from smaller environmental and centrist parties. But it is thought likely that Mr. Sarkozy and Mr. Hollande will face off in the final round on May 6.
The Socialists are eager for power. Since 1958, they have elected only one president, François Mitterrand, and he left office more than 16 years ago. But with Mr. Sarkozy’s popularity so low, the Socialists can taste victory, and in France the near-royal presidency carries with it many spoils. A loss this time would cause an enormous internal fight.
Mr. Hollande, born in Rouen, the son of a doctor and a social worker, has said the country needs “a normal president,” a backhanded slap at Mr. Sarkozy, who has a driven, relentless personality and who has embroiled the French more in his personal life than many people find comfortable. At 56, he is awaiting the birth of a child with his third wife, the singer Carla Bruni-Sarkozy.
Mr. Hollande is intelligent and witty, educated at France’s most elite schools, but inexperienced in government, as his rivals constantly point out. He was Ms. Aubry’s predecessor as leader of the Socialist Party and was close to Ms. Aubry’s father, Jacques Delors, but he has never been a government minister or run a business. He is a member of Parliament and the president of the regional department of Corrèze, a rural area best known for its connections to former President Jacques Chirac, with whom Mr. Hollande has warm relations.
Mr. Hollande inherited a region steeped in debts, many of them from Chirac-initiated infrastructure projects, and is considered to have managed the budget well. But Corrèze is one of the smallest departments in France and does not really compare with governing a nation that sits on the United Nations Security Council, possesses nuclear weapons and is the only country in the world, besides the United States, to have a nuclear-powered aircraft carrier.
Foreign affairs barely entered the Socialist Party’s primary and its televised debates, and Mr. Hollande is considered something of a work in progress. But foreign policy, which Mr. Sarkozy considers one of his strengths, is a prime prerogative of the French president.
The Socialist contest was always an odd one, because the putative favorite for the nomination — Dominique Strauss-Kahn, the former managing director of the International Monetary Fund — did not run after he was arrested on charges of attempted rape in New York. The charges were dropped, but Mr. Strauss-Kahn retreated from political life.
Ms. Aubry had made a deal with Mr. Strauss-Kahn that she would not run if he did, so in a sense she was an accidental candidate. Mr. Hollande had declared his candidacy from the outset, positioning himself as the main rival to Mr. Strauss-Kahn. A centrist, emollient figure, Mr. Hollande was the natural inheritor of those who supported the center-right Strauss-Kahn, but Ms. Aubry attacked him as “soft” and “vague.”
Mr. Hollande for many years was the partner of Ségolène Royal — his rival for the Socialist candidacy in 2007, which she won — and they have four children together. They separated that year, and Mr. Hollande now lives with a political journalist, Valérie Trierweiler, 46, who is divorced with three children. Ms. Trierweiler is said to not relish the idea of being the partner to a French president. This month the government denied reports that it was investigating her private life.
This primary was a departure for the Socialists, in that voting was open to any French citizen who paid at least one euro ($1.39) and signed a pledge to support “the values of the left and of the republic.”
About 2.7 million people voted on Oct. 9, when Mr. Hollande won 39 percent of the vote to Ms. Aubry’s 31 percent, forcing a runoff. About the same number, 2.7 million, are thought to have voted in Sunday’s second round. By comparison, more than 36.7 million people voted in the first round of the 2007 presidential contest.
Still, the Socialists called the primary a democratic advance, contrasting it to the backroom deals that resulted in Mr. Sarkozy’s becoming the candidate of his party. While the number of voters in this primary may have been relatively modest, many more watched last Wednesday’s televised Socialist debate.
Nicola Clark contributed reporting.
Après bien des 
DÉMOCRATIE PARTICIPATIVE 