Mr. Sarkozy trails in the polls, but he could not deliver the clear victory in this debate that many analysts thought he needed to win the election. Mr. Hollande, trying to undermine a reputation for softness and charm, was an aggressive debater, often interrupting Mr. Sarkozy without deference and seemingly even with contempt.

Mr. Hollande attacked Mr. Sarkozy for favoring the rich, for self-satisfaction and for blaming anyone and everything but himself for France's problems, in particular its low economic growth and high unemployment. "With you it's simple, it's always someone else's fault," Mr. Hollande said. "You always have a scapegoat."

"I protect the children of the republic, and you, you protect the most privileged," Mr. Hollande said.

Mr. Sarkozy responded that he had no love for the rich.

"The difference between us," he said, "is that you want fewer rich and I want fewer poor." He attacked Mr. Hollande for his vague economic policies, at one point describing them as "your spending craze" and saying that the Socialists only spoke of new taxes and public spending and never any cuts.

"You say you're going to save money?" Mr. Sarkozy demanded of Mr. Hollande, and then made an incredulous face. "Oh, really?"

Mr. Sarkozy, exasperated at one charge of partisanship, burst out: "That's a lie, it's a calumny, you are a little calumniator, saying that." And at one point, he said to Mr. Hollande: "Thank you for your arrogance."

Mr. Hollande attacked the president for political partisanship, and Mr. Sarkozy fiercely responded, "I will take no lessons from a political party who wanted with enthusiasm to come together behind Dominique Strauss-Kahn." He accused Mr. Hollande, who had run the Socialist Party, of being Pontius Pilate when he claimed not to have known of Mr. Strauss-Kahn's sexual predilections. Mr. Hollande said that it was Mr. Sarkozy who nominated Mr. Strauss-Kahn as director of the International Monetary Fund.

The debate went on passionately for nearly three hours, with the two television journalists who were to moderate it looking nearly paralyzed as the insults and interruptions flew between the two men, each 57, each dressed in a dark blue suit, white shirt and dark blue tie. The set was a carefully negotiated plexiglass monstrosity, with a slide of the Élysée Palace in the background and two large digital clocks measuring the time each man spoke. About 20 cameras were used on a set that had been kept cool, by agreement, to 66 degrees.

As hot as the language was, it is not clear if the debate will change the minds of many voters before Sunday.

Frédéric Dabi, the director of the polling firm IFOP, said that a search of his company's archives yielded a simple lesson: "The debate serves simply to anchor people a little more in their convictions," Mr. Dabi told LeMonde. If public opinion moves a little, as it did in the fierce 1988 debate between François Mitterrand and Jacques Chirac, he said, "it's not a big thing."

Emmanuel Rivière of TNS Sofres said that in the 2007 debate between Mr. Sarkozy and the Socialist challenger, Ségolène Royal, which Mr. Sarkozy was acknowledged to have won, Ms. Royal fell a couple of percentage points in the polls, but then gained most of it back before the vote.

The only debate considered to have mattered in a tight French election was in 1974, when Valéry Giscard d'Estaing was considered to have won when he told François Mitterrand: "You do not have the monopoly of the heart."