"We are rid of a poison that was blighting our society. A normal president? ..He should give 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.
Mr Hollande led in opinion polls throughout the campaign and won the April 22 first round with 28.6 per cent to Mr Sarkozy's 27.2 per cent - 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 per cent at 5pm (1am AEST), 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 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 to make it focus more on growth, but is facing resistance from Merkel.
Mr Hollande has already flagged his displeasure with the existing austerity plan, he has suggested that the top end of town should contribute more, rather than just placing the burden on average workers.
This way more could be spent on job creation and boosting business investment.
Without some stimulus there will be no improvement in productivity or growth says Mr Hollande.
Apparently many governments in Europe agree that the austerity program needs tweeking, it has not helped to increase productivity or create growth,weather Mr Hollande can convince Angela Merkel is another story.