Nicolas Sarkozy 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.
Francois Hollande and Nicolas Sarkozy 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%.
Francois Hollande’s narrow victory in this round gives him crucial momentum ahead of the run-off in two weeks’ time.
Nicolas Sarkozy, leader of the ruling centre-right UMP, will now need to woo the far-right voters who backed Marine Le Pen if he is to hold on to the presidency. But Francois Hollande remains the front runner.
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.
The election has been dominated by economic issues, with voters concerned with sluggish growth and rising unemployment.
Marine 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 Nicolas Sarkozy in the second round.
But pollsters also predict a large abstention rate in the second round.
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 Francois 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 Nicolas 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,” Francois 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.
Nicolas 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.
Francois 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%.
Marine 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 Francois Hollande in the run-off.
Centrist Francois Bayrou, who was hoping to repeat his high 2007 score of 18%, garnered only about 9%.
If Nicolas 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.
Nicolas Sarkozy has promised to reduce France’s large budget deficit and to tax people who leave the country for tax reasons.
Francois Hollande has strongly criticized Nicolas Sarkozy’s economic record.
The Socialist candidate has promised to raise taxes on big corporations and people earning more than 1 million 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, Francois Hollande would be France’s first left-wing president since Francois Mitterrand, who completed two seven-year terms between 1981 and 1995.
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