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."
Greek election result far more "dangerous" than Francois Hollande.
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.
I think we are going to see the eurozone yet further challenged very seriously and I think that what you will see both from France and from Germany is a very united response.
I think that both from Mr Hollande and Mrs Merkel you are going to see the top priority being stopping the eurozone from splitting.
I think that you will see both of them saying that everything that needs to be done to save the whole post war settlement in Europe, as well as the euro, will require more European integration, not less. It will require more Europe, not less.
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:
Your victory has given all socialist sister parties across Europe great hope for the future - hope that there is an alternative and principled way forward during these difficult financial and economic times.
I am proud that France and Wales have many things in common - not least our shared passion for rugby. I look forward to welcoming you to Cardiff, when France next play Wales.
The Prime Minister has congratulated France's President-Elect Francois Hollande for his victory in the elections. A Number 10 spokesperson said:
– Number 10 Spokesperson
The Prime Minister called President-Elect Hollande this evening and congratulated him on his victory.
They both look forward to working very closely together in the future and building on the very close relationship that already exists between the UK and France.”