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.