French President Nicolas Sarkozy faces an uphill struggle in the second round of the presidential election, after coming second in Sunday's first vote.
He won 27.1% of the vote, while his Socialist rival Francois Hollande took 28.6%, the first time a sitting president has lost in the first round.
The two men will face each other in a second round of voting on 6 May.
Third-place Marine Le Pen took the largest share of the vote her far-right National Front has ever won, with 18%.
The BBC's Christian Fraser in Paris says Mr Hollande's narrow victory in this round gives him crucial momentum ahead of the run-off in two weeks' time.
Analysts suggest Mr Sarkozy, leader of the ruling centre-right UMP, will now need to woo the far-right voters who backed Ms Le Pen if he is to hold on to the presidency. But Mr Hollande remains the front runner.
Mr Sarkozy began reaching out to Ms Le Pen's voters on Monday, saying "there was this crisis vote that doubled from one election to another - an answer must be given to this crisis vote".
Around one in five people voted for the National Front candidate, including many young and working class voters, putting her ahead of seven other candidates.
How many debates?
The election has been dominated by economic issues, with voters concerned with sluggish growth and rising unemployment.
Ms Le Pen, who campaigned on a nationalist, anti-immigration platform, said she would wait until May Day next week to give her view on the second round.
She told jubilant supporters that the result was "only the start" and that the party was now "the only opposition" to the Left.
Opinion polls taken after voting on Sunday suggested that between 48 and 60% of Le Pen voters would switch to backing Mr Sarkozy in the second round.
But pollsters also predict a large abstention rate in the second round.
The BBC's Europe editor Gavin Hewitt says the result revealed a dissatisfaction and restlessness in France, creating political volatility. The elites are despised, the economic future is feared and there is insecurity, he says.
Nearly a fifth of voters backed a party - the National Front - that wants to ditch the euro and return to the franc.
But polls suggest Mr Hollande will comfortably win the second round.
As the results came in, he said he was "best placed to become the next president of the republic" and that Mr Sarkozy had been punished by voters.
"The choice is simple, either continue policies that have failed with a divisive incumbent candidate or raise France up again with a new, unifying president," Mr Hollande said.
It is the first time a French president running for re-election has failed to win the first round since the start of the Fifth Republic in 1958.
Mr Sarkozy - in power since 2007 - said he understood "the anguish felt by the French" in a "fast-moving world".
He called for three debates during the two weeks to the second round - centring on the economy, social issues, and international relations.
Mr Hollande promptly rejected the idea. He told reporters that the traditional single debate ahead of the second round was sufficient, and that it should "last as long as necessary".
Turnout on Sunday was high, at more than 80%.
Ms Le Pen achieved more than the breakthrough score polled in 2002 by her father and predecessor, Jean-Marie Le Pen, who got through to the second round with more than 16%.
Leftist candidate Jean-Luc Melenchon, who was backed by the Communist Party, came fourth with almost 12%.
He urged his supporters unconditionally to rally behind Mr Hollande in the run-off.
Centrist Francois Bayrou, who was hoping to repeat his high 2007 score of 18%, garnered only about 9%.
The BBC's Chris Morris in Paris says that if Mr Sarkozy cannot change the minds of a substantial number of people, he will become the first sitting president to lose an election since 1981.
Wages, pensions, taxation, and unemployment have been topping the list of voters' concerns.
President Sarkozy has promised to reduce France's large budget deficit and to tax people who leave the country for tax reasons.
Mr Hollande has strongly criticised Mr Sarkozy's economic record.
The Socialist candidate has promised to raise taxes on big corporations and people earning more than 1m euros a year.
He also wants to raise the minimum wage, hire 60,000 more teachers and lower the retirement age from 62 to 60 for some workers.
If elected, Mr Hollande would be France's first left-wing president since Francois Mitterrand, who completed two seven-year terms between 1981 and 1995.