France's presidential election was a close-run affair, far closer than the polls had suggested through most of the long and often ill-tempered campaign. So, while François Hollande's victory gives France its first Socialist President for 16 years and makes Nicolas Sarkozy France's first one-term President for more than a generation, it represents something less than the historic turnaround Mr Hollande's supporters rushed to claim. France, like so many European countries, remains finely balanced between left and right. A crisis such as the one that it, and the Continent as a whole, faces, is not resolved by an election; in some ways, an election merely highlights the divisions.

Whoever won this election was always going to find that his room for manoeuvre was limited. The money is simply not there to spend on pet projects and lavish promises, while the constraints of euro membership – even at a time when those constraints seem more fluid – narrow the options again. But the size of Mr Hollande's majority adds a further damper. It turns out that, when they actually reached the polling booth, French voters were less sure about the wisdom of evicting Mr Sarkozy than they had been. Experience of high office and crisis-management suddenly looked more valuable than it had done during the heat of electoral battle. They are parting with the mercurial Mr Sarkozy, but not – it appears – without a tinge of regret.

Yet the election of François Hollande, despite all the limits on his authority and capacity for action, does convey a sense of change, albeit of emphasis rather than overall direction. The political map of France has gone, overnight, from blue to red, and this must fuel expectations, not just in France, but across the continent. At best, the shift could embolden politicians to pursue remedies to the economic crisis in new, more imaginative ways, rather than relying only on cuts.

Mr Hollande's central promises were on state spending, jobs and education. More teachers and a needed revamp of state schools in disadvantaged areas could be his first test, as he tries to make an early mark. Like previous newly elected French presidents, he is expected to rush to meet the German Chancellor, to scotch any speculation about worsening relations. At home, he will quickly come under pressure from the left to show his colours. Even if the Socialists have a majority in the National Assembly after legislative elections in June, the far left and far right are also likely to be represented, complicating the new President's need to occupy the political centre ground. An autumn of discontent is predicted, as the trade unions flex their muscles. If, as it appears, Mr Hollande won French minds, but not their hearts, he may be in for a hard time.

As for Mr Sarkozy, his defeat may well have been a rejection of his personality. But it also poses once again the question of whether any national leader, of any party, can impose the degree of austerity deemed necessary by the financial markets and remain electable. Ireland's ruling party, Fianna Fail, was erased in a landslide early last year. Silvio Berlusconi resigned last November, making way for a technocratic government in Italy; Spain ousted its Socialist government only days later. Early results in yesterday's Greek elections showed the larger parties routed, as voters called down a plague on those they held responsible for the country's economic plight. Only Poland has bucked the trend so far, and no member of the eurozone.

Mr Hollande's challenge will be to show that a leader who owes his election to the crisis can carry the people with him. Otherwise he, like Mr Sarkozy today, will be asking what he might have done differently five years hence.