Francois Hollande got about 52% of votes in today’s run-off, according to projections based on partial results, against 48% for centre-right incumbent Nicolas Sarkozy.
He would be the first French socialist president since 1995.
Analysts say the vote has wide implications for the whole eurozone.
Francois Hollande has vowed to rework a deal on government debt in member countries.
The estimates were carried by French media after all polling stations closed at 20:00.
Exuberant Hollande supporters have already converged on Place de la Bastille in Paris – a traditional rallying point of the Left – to celebrate.
Francois Hollande capitalized on France’s economic woes and President Nicolas Sarkozy’s unpopularity.
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.
Nicolas Sarkozy, a centre-right leader who has been in office since 2007, had promised to reduce France’s large budget deficit through budget cuts.
It is only the second time an incumbent president fails to win re-election since the start of France Fifth Republic in 1958.
The last was Valery Giscard d’Estaing – he 1981 was beaten by socialist Francois Mitterrand, who had two terms in office until 1995.
The new president is expected to be inaugurated later this month.
A parliamentary election is due in June.
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