This is disturbing news, to say the least. Hollande ran on a platform calling for more stimulus spending and he won. Are these people crazy? Are they intent on collapsing their economy? Of course, our leftist leader has already invited the Socialist to the White House. "I think this is the beginning of a beautiful friendship."
Europe is turning left but America must turn right in November! Yes, it is too late to put a conservative at the top of the GOP ticket but all of the House and one third of the Senate is in play and conservatives can be elected in those seats. - Reggie
Mr Hollande - who polled just under 52% of votes in Sunday's run-off - spoke of his pride at becoming president.
Admitting defeat, centre-right incumbent Nicolas Sarkozy wished "good luck" to Mr Hollande.
Analysts say the vote has wide implications for the whole eurozone. Mr Hollande has vowed to rework a deal on government debt in member countries.
Shortly after polls closed at 20:00 (18:00 GMT), French media published projections based on partial results giving Mr Hollande a lead of almost four points. Turnout was about 80%.
Jubilant Hollande supporters gathered on Place de la Bastille in Paris - a traditional rallying point of the Left - to celebrate.
People drank champagne and chanted: "Sarko, it's over!"
Mr Hollande - the first Socialist to win the French presidency since Francois Mitterrand in the 1980s - gave his victory speech in his stronghold of Tulle in central France.
He said he was "proud to have been capable of giving people hope again".
He said he would push ahead with his pledge to refocus EU fiscal efforts from austerity to "growth".
"Europe is watching us, austerity can no longer be the only option," he said.
After his speech in Tulle, Mr Hollande headed to Brive airport on his way to Paris to address supporters at Place de la Bastille. His voice hoarse, he spoke of his pride at taking over the mantle of the presidency 31 years almost to the day since Socialist predecessor Francois Mitterrand was elected.
"I am the president of the youth of France," he told the assembled crowd of tens of thousands of supporters, emphasising his "pride at being president of all the republic's citizens". "You are a movement that is rising up throughout Europe," he said.
Mr Hollande has called for a renegotiation of a hard-won European treaty on budget discipline championed by German Chancellor Angela Merkel and Mr Sarkozy.
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