"Tonight France is back in Europe," Nicolas Sarkozy said in his victory speech, on the night of his election on 6 May.
By Stephen Mulvey
EU reporter, BBC News
He said he had believed deeply and sincerely in the construction of Europe all his life.
But in the next breath, he warned Europe to listen to French citizens who saw Europe as an enemy of social protection and a Trojan horse of "all the threats that come with the changes in the world".
Mr Sarkozy's admiration for British deregulation has a very Gallic edge
These comments encapsulate the hopes and fears that other European leaders have regarding Mr Sarkozy's influence on the EU.
The arrival of a vigorous new president in France means that the EU can now start taking real steps to resolve the problems caused by the French rejection of the draft constitution in a referendum two years ago.
Mr Sarkozy is in favour of a quick solution, and he wants to avoid a referendum. This is music to the ears of both Germany and the UK - Germany as the country in charge of getting the constitution back on track at a summit in June, and the UK as a country seeking to avoid its own referendum at all costs.
There are even those who talk about a "dream team" of young-ish European leaders - Angela Merkel, Nicolas Sarkozy, Gordon Brown and Commission President Jose Manuel Barroso.
The team is supposed to be economically liberal, and to have pro-American instincts. It is ready to shake Europe up, grasp the challenges of globalisation, and to put climate change at the top of the agenda.
But there are many who question how neatly Mr Sarkozy fits into this picture, pointing out that his admiration for British free markets has a very Gallic edge.
He wants the EU to have an industrial policy, is uneasy with the idea of an independent Central Bank, and has called on the EU to protect citizens from "unfair" competition from abroad, particularly in Asia.
He has demanded protection from various kinds of dumping - fiscal, social and environmental - from poorer EU member states in eastern Europe. The "Polish plumber" returned to France for the election campaign.
In Brussels, memories are also fresh of the state-funded bail-out of Alstom Mr Sarkozy persuaded the Commission to accept in 2004 - and of his subsequent crowing about defending French jobs in the face of opposition from regulators.
So could he turn out to be another difficult and bossy Gaullist?
"He is like Jacques Chirac, only worse," Daniel Gros, director of the Centre for European Policy Studies told one British newspaper.
Turkey and the CAP
One Sarkozy policy that will definitely create waves is his determined opposition to Turkish EU membership.
One adviser says France will demand an agreement on "stable" borders for Europe - which is to say, borders which do not include Turkey - before doing any final deal on the European constitution.
One surprising area where Mr Sarkozy and Gordon Brown may find some common ground is the Common Agricultural Policy, which is up for review, with the rest of the EU budget, next year.
France, currently the biggest recipient of CAP funds, knows that the balance sheet will look very different when the CAP is fully extended to the new member states from central and eastern Europe.
The man tipped to be Mr Sarkozy's Europe Minister, Alain Lamassoure, therefore favours shifting the responsibility for paying some farm subsidies from Brussels to the individual member states.
On the European constitution, Mr Sarkozy occupies a position somewhere in between the maximalists, such as Germany - who would like the new text to mirror the old one as closely as possible - and the minimalists, such as the UK, who want as few changes as possible to the existing EU treaties.
While Mr Sarkozy was the first to talk of a "mini-treaty", his team have made clear that he still envisages sweeping away a lot of national vetoes, transferring sovereignty to the EU.
Mr Sarkozy's arrival, in itself, allows the EU to move up a gear after a period of stagnation, and his energetic personality could be a breath of fresh air.
But it seems clear that the new French leader will not solve Europe's many problems overnight, and could even make them more intractable.