This in turn poses a problem for Sarkozy's own party, the UMP. First, with Sarkozy's defeat, there is very little, if anything, that remains of historic Gaullism. Next, Sarkozy's departure opens up the way for what could be a lengthy and bitter struggle to secure the leadership of the movement. If former prime minister François Fillon looks well-placed, there is no clear candidate to head the party. Since the defeat of the second ballot all the talk has been about unity but this cannot hide the many tensions and rivalries. A split cannot be ruled out. In particular, the UMP faces the challenge of parliamentary elections in June where the political imperative is that of limiting the success of the socialists. This is where Le Pen comes in, and where the UMP faces an acute dilemma.

Like presidential elections, parliamentary elections in France are decided by two ballots. French electoral law stipulates that any candidate obtaining more than 12.5 per cent of the vote can stand again in the second ballot. On the basis of polling in the first round of the presidential election, it is estimated that as many as 350 Front National candidates might present themselves. In contrast there was only one candidate as recently as 2007. The dilemma facing the UMP is whether, in these circumstances, it contemplates an electoral pact with Marine Le Pen's party. If it does not, it faces heavy losses. If it does, it risks further strengthening the Front National and weakening its own position as the dominant party on the Right. More fundamentally, the choice will determine whether the UMP positions itself as liberal and republican or anti-European and nationalist. The indications are that a majority of UMP voters favour an alliance with the Front National.

The political dilemmas facing Hollande are of a different nature. At present the Socialist Party holds 186 seats in the National Assembly. It needs 289 to secure an absolute majority. The electoral boost provided by Hollande's victory looks set to deliver those seats. However, on his Left Hollande faces the Front de Gauche and the rather troublesome character of Jean-Luc Mélenchon, the big loser of the first round. Mélenchon made the mistake of believing his own propaganda and staked all on coming ahead of Marine Le Pen. As it was, he secured only 11.11 per cent of the vote and came in a poor fourth. 

But Mélenchon tells us a lot about the unchanging character of a significant part of the French Left. Without embarrassment, he proclaims himself to be "completely Jacobin, revolutionary, republican and French". At his rallies, women dress as Liberty and wear the Phrygian bonnet. Few of Mélenchon's supporters voted for Hollande but they will seek to ensure that he steers as left-wing a course as possible. How long Hollande can keep such unreconstructed leftists on board is an open question.

Hollande also has to ensure that his party makes the transition from opposition to government. This is especially difficult for parties of the Left, for whom the responsibilities of power usually come at a heavy price. Hollande will need to balance carefully the demands of traditionalists and modernisers within his party leadership, and also withstand potential clashes between an older and a younger generation. No less difficult to decide is the role to allot to Ségolène Royal.