I have been listening to, on the BBC World Service, Sarkozy giving his concession speech.
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.
The socialist candidate has promised to raise taxes on big corporations and people earning more than 1m euros a year.
He also wants to raise the minimum wage, hire 60,000 more teachers and lower the retirement age from 62 to 60 for some workers.
Can France support these new economic initiatives? What effect will his victory have on the rest of Europe?
From a BBC profile of Hollande:
Mr Hollande is generally viewed as a moderate.
“I don’t want a hard left,” he said during a debate with Martine Aubry, his main rival for the socialist presidential nomination.
He may come across as a moderate but Mr Hollande chose to fight his campaign on some hard-hitting economic policies, with proposals for a 75% top rate of tax and the recruitment of 60,000 new teachers. He has also vowed to renegotiate the EU’s fiscal growth pact, signed by President Sarkozy.
The idea of a 75% income tax rate for earnings above 1m euros (£820,000; $1.3m) appeared to take his colleagues by surprise and was widely condemned by his rivals. The head of Mr Sarkozy’s UMP party, Jean-Francois Cope, labelled his proposal for thousands of extra teachers as “crazy”.