Hollande got about 28 percent of votes Sunday, according to projections based on partial results, against about 26 percent for centre-right incumbent Nicolas Sarkozy.
The two men will face each other in a second-round run-off May 6. It is the first time a French president running for re-election failed to win the first round since the start of the Fifth Republic in 1958, the BBC reported. The election has been dominated by widespread anxiety over the French economy and the wider eurozone crisis.
The estimates - based on votes counted in polling stations that closed early at 6.00 p.m. - were announced by French media when all voting ended at 8.00 p.m. Sarkozy - who has been in power since 2007 - was facing a total of nine candidates in Sunday's first round. Far-right leader Marine Le Pen came third with about 20 percent of the vote - more than the breakthrough score achieved by her father and predecessor, Jean-Marie Le Pen in 2002, when he got through to the second round with almost 17 percent.
Leftist candidate Jean-Luc Melenchon came fourth in Sunday's vote with more than 11 percent. Centrist Francois Bayrou, who was hoping to repeat his high 2007 score of 18 percent, garnered only about nine percent. There was a high turnout, estimated at about 80 percent, according to BBC. President Sarkozy has promised to reduce France's large budget deficit and to tax people who leave the country for tax reasons.
He has also called for a "Buy European Act" for public contracts, and threatened to pull out of the Schengen passport-free zone unless other members do more to curb immigration from non-European countries. Hollande has strongly criticised Sarkozy's economic record. The Socialist leader has promised to raise taxes on big corporations and people earning more than one million euros ($1.3 million) a year, the BBC said.
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