“How Hollande handles Merkel could make or break his prospects for the next five years,” said François Heisbourg of the Foundation for Strategic Research in Paris. “He has favorable circumstances, but she has domestic politics, too,” he said, and she is seen as likely to agree only to symbolic changes in the fiscal pact — not renegotiating it so much as adding clauses about growth to it.

Mr. Hollande, who may take over as president as early as May 14, will have little time to relax. He must travel to the United States for a meeting of the Group of 8 industrialized countries on May 18-19 and then a NATO summit meeting in Chicago on May 20-21, where he intends to make good on his promise to pull French combat troops out of Afghanistan by the end of this year, and where American and NATO officials will try to get him to change his mind.

Mr. Hollande’s victory will also have important implications for the right in France, with Mr. Sarkozy’s party already split between the prime minister, François Fillon, and the Sarkozy-like party leader, Jean-François Copé. The strong showing of Marine Le Pen of the National Front, who got nearly 18 percent of the vote in the first round of the presidential election, is a serious threat to Mr. Sarkozy’s party. It now must decide whether to make a deal with Ms. Le Pen for assembly seats in the second round of the legislative election; if not, the Union for a Popular Movement could lose up to 100 seats, political experts say.

Mr. Hollande campaigned on “change” and a more traditional presidency, where he would set the main course of policy but not micromanage day-to-day affairs, as Mr. Sarkozy did.

For the French, “it is a leap of faith that shows there is a strong will for a different policy course, not just at the national but at the E.U. level as well,” said Paul Vallet, a professor of history and political science at the Paris-based Institut d’Études Politiques.

The indebted countries of Europe are also hoping that Mr. Hollande can be a champion buying them more time to adjust. “Some countries in Europe are banking on that,” Mr. Vallet said.