Updated 8.45 p.m.

Socialist Francois Hollande has declared victory in France's presidential election, railing against austerity measures and urging national unity after a bitter campaign against Nicolas Sarkozy.

The mild-mannered Mr Hollande promised help for France's downtrodden after years under the tough-talking Mr Sarkozy, a man many voters blamed for economic troubles.

Mr Hollande says austerity should no longer be inevitable and said European partners should be relieved and not frightened by his presidency.

Mr Hollande told huge crowds of supporters in his electoral fiefdom of Tulle in central France that he was "proud to have been capable of giving people hope again. We will succeed!"

Hollande was elected France's first Socialist president in nearly two decades, dealing a humiliating defeat to Sarkozy and shaking up European politics.

The result will have major implications for Europe as it struggles to emerge from a financial crisis and for France, the eurozone's second-largest economy and a nuclear-armed permanent member of the UN Security Council.

Socialist Party (PS) newly elected president Francois Hollande poses flanked by his companion Valerie Trierweiler this evening.

Hollande won the vote with about 52 percent, according to several estimates from polling firms based on ballot samples, becoming France's first Socialist president since Francois Mitterrand left office in 1995.

Joyful crowds gathered in Hollande's adopted hometown of Tulle and in Paris to celebrate his victory.

"We are rid of a poison that was blighting our society. A normal president! It gives us a lot to dream about," said Didier Stephan, a 70-year-old artist who was among throngs of supporters at Paris's Place de la Bastille.

Even before polls closed and broadcasters released estimates, supporters were chanting "President Hollande!" and "We Won!" at the iconic square.

Sarkozy urged leaders of his right-wing UMP party to remain united after his defeat, but warned he would not lead it into June's parliamentary elections, according to political sources present at a meeting at his headquarters.

Hollande led in opinion polls throughout the campaign and won the April 22 first round with 28.6 percent to Sarkozy's 27.2 percent -- making the right-winger the first-ever incumbent to lose in the first round.

Grey skies and rain showers greeted voters across much of France, but turnout was high, hitting 71.96 percent at 5:00 pm (1500 GMT) according to interior ministry figures. More than 46 million people were eligible to vote.

The election was marked by fears over European Union-imposed austerity and economic globalisation, and Hollande has said his first foreign meeting will be with German Chancellor Angela Merkel -- the key driver of EU budget policy.

The 57-year-old Socialist has vowed to renegotiate the hard-fought fiscal austerity pact signed by EU leaders in March and to make it focus more on growth, but is facing resistance from Merkel.

The French vote coincides with an election in Greece, where voters were also expected to punish the incumbent parties for landing the country in its bleak economic state.

Celebrations in Paris this evening.

Anger over sputtering economies has brought down leaders from Ireland to Portugal since the debt crisis washed over the European continent.

Hollande has said he will move quickly to implement his traditionally Socialist tax-and-spend programme, which calls for boosting taxes on the rich, increasing state spending and hiring some 60,000 teachers.

Sarkozy fought a fierce campaign, saying a victory for Hollande would spark market panic and financial chaos and calling him a "liar" and "slanderer" in the final days of the race.

But Sarkozy failed to overcome deep-rooted anger at meagre economic growth and increasing joblessness, and disappointment after he failed to live up to the promises of his 2007 election.

Sarkozy, 57, was also deeply unpopular on a personal level, with many voters turned off by his flashy "bling bling" lifestyle -- exemplified by his marriage to former supermodel Carla Bruni -- and aggressive behaviour.

Hollande has vowed to be a "normal president" in contrast with Sarkozy, but some have raised concerns over his lack of experience.

Hollande, a long-time Socialist party leader and local lawmaker from the central Correze region, has never held a top government post.

The first round of the election last month was marked by a record score for Marine Le Pen of the far-right, anti-immigrant and anti-Europe National Front, when she took nearly 18 percent of the vote.

Sarkozy turned increasingly to the right ahead of the run-off -- vowing to restrict immigration and "defend French values" -- but Le Pen refused to call on her supporters to back him and she cast a blank ballot.

Hollande won the backing of centrist Francois Bayrou, who took nine percent in the first round, and Communist-backed Jean-Luc Melenchon of the Left Front, who took 11 percent.

"This is a very big failure (for Sarkozy) against a candidate who has no experience in government," said political analyst Stephane Rozes.

"It is not so much for the content of his policies that he has been punished, but for his way of being and acting," Rozes said.

Hollande is expected to be sworn in by May 15 and after seeing Merkel will quickly set off for a series of international meetings, including a G8 summit in the US on May 18-19 and NATO gathering in Chicago on May 20-21.

The Socialists, Sarkozy's right-wing UMP and France's other political parties will now be focused on a parliamentary election to be held over two rounds on June 10 and June 17.