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Francois Hollande will be inaugurated as France's new President on 15 May.
The European Union's fiscal compact is not up for renegotiation, German Chancellor Angela Merkel said
Hollande has criticised Germany's heavy emphasis on austerity to tackle Europe's sovereign debt crisis and has called for policies to revive economic growth.
But Merkel told a news conference: "We in Germany are of the opinion, and so am I personally, that the fiscal pact is not negotiable. It has been negotiated and has been signed by 25 countries.
"We are in the middle of a debate to which France, of course, under its new president will bring its own emphasis. But we are talking about two sides of the same coin -progress is only achievable via solid finances plus growth."
Former EU commissioner Lord Mandelson told the BBC Radio 4 Today programme that he expected Mr Hollande and Mrs Merkel to mount a renewed push for greater EU integration in order to shore up the eurozone.
Crowds in Bastille after victorious Socialist Francois Hollande thanked his supporters for voting him in as the new president of France and told them they are leading a Europe-wide movement against austerity.
President Barack Obama has called newly elected French President Francois Hollande to congratulate him on his victory.
Obama called Hollande and "indicated that he looks forward to working closely" with him and his government on a "range of shared economic and security challenges," the White House said in a statement.
In a letter, Welsh First Minister Carwyn Jones congratulated Mr Hollande on his "superb and historic" election:
The Prime Minister has congratulated France's President-Elect Francois Hollande for his victory in the elections. A Number 10 spokesperson said:
Latest ITV News reports
France's capital is back to normal after a night of celebrations for the new president. But France's politics looks very different today.
Francois Hollande is elected France's new president. He received 52% of the vote against 48% for Nicolas Sarkozy, according to projections.