Hollande was set to beat conservative incumbent Nicolas Sarkozy by a decisive 51.9 percent to 48.1 percent margin, the TNS-Sofres polling agency said in a projection based on a partial vote count.
The President conceded defeat within 20 minutes of the last polls closing at 8 pm (1800 GMT), telling supporters he had telephoned Hollande to wish him good luck. "I bear the full responsibility for this defeat," he said.
Sarkozy, punished for his failure to rein in record 10 per cent unemployment and for his brash personal style, is the 11th successive leader in the euro zone to be swept from power since the currency bloc's debt crisis began in 2009.
Jubilant left-wingers celebrated outside Socialist Party headquarters and in Paris' Bastille square, where revelers danced in 1981 when Francois Mitterrand became France's only other Socialist president.
But the celebrations may be overshadowed by a political bombshell in Greece, where mainstream parties were hammered in a parliamentary election that exit polls suggested may leave supporters of Athens' IMF/EU bailout without a majority, raising doubts about its future in the euro zone.
Hollande's clear win should give the self-styled "Mr Normal" the authority to press German Chancellor Angela Merkel to accept a policy shift towards fostering growth in Europe to balance the austerity that has fueled anger across southern Europe. His margin also positions the Socialists strongly to win a left-wing majority in parliamentary elections next month, vital to implement his plans for a swift tax reform.
If it wins that two-round election on June 10 and 17, the Socialist Party would hold more levers of power than ever in its
43-year history, with the presidency, both houses of parliament, nearly all regions, and two-thirds of French towns in its hands. Even before the results were declared, cheering crowds gathered at Socialist headquarters to acclaim the party's first presidential victory since Mitterrand's re-election in 1988.
Many waved red flags and some carried roses, the party emblem. In Bastille square, flashpoint of the 1789 French Revolution and the left's traditional rallying point
for protests and celebration, activists began partying two hours before the polls closed and a swelling
crowd cheered as giant TV screens relayed the results. — Reuters