IN THE closing days of the campaign, before the French went to the polls to choose a new president on May 6th, Nicolas Sarkozy was clinging to two hopes. First, that the televised debate with François Hollande, his Socialist challenger, on May 2nd would reveal the value of his experience and expose his rival's lack of it. And second, that his strategy of chasing the far-right vote would pay off. With the National Front's Marine Le Pen pointedly refusing to endorse Mr Sarkozy, however, and with the polls consistently making Mr Hollande the favourite, neither hope looked likely to rescue the incumbent from defeat.

Face-to-face with Mr Hollande in a television studio, and watched by nearly 18m viewers, Mr Sarkozy put in a feisty performance. He drew on some of the themes that have marked his second-round campaign, in an appeal to the 18% of voters who had turned to Ms Le Pen in the first round, including the need to curb immigration. He also nodded to the 9% of centrist voters who had backed François Bayrou by arguing that curbing the debt and the deficit were the only ways for France to “master its destiny” and avoid a fate like Spain's.

But if he had hoped to unsettle Mr Hollande it was to no avail. The Socialist kept his nerve, dodged tricky questions and held his own against Mr Sarkozy's repeated charge that he was lying. The so-called Mr Normal was unruffled by Mr Sarkozy's charge that his “normality does not measure up to what is at stake.” He cleverly turned the economic debate back to Mr Sarkozy's record. Doubts about Mr Hollande's solidity were allayed by his firm grasp of detail, and a refusal to be browbeaten. The final vote may turn out closer than suggested by the latest polls, which give Mr Hollande victory by six to eight points. But, as with previous presidential debates, this one seems unlikely to change the outcome.

Arithmetically, Mr Sarkozy's best chance is still to hope for a huge chunk of National Front voters. On paper, it might look as if they should swing behind him, just as on the left the vast majority of those who backed a revolutionary firebrand, Jean-Luc Mélenchon, will support Mr Hollande. But this is to misunderstand both the nature of the party's vote and Ms Le Pen's endgame. She drew support from a mixed bag of the discontented: not just xenophobes, but Catholic traditionalists, ex-communists and industrial workers fearful of globalisation, job losses and the euro, and disillusioned by France's ruling elite. In the first round, she came first among working-class voters. Although between 43% and 57% of her supporters say that they will back Mr Sarkozy in the run-off, some 15-21% prefer Mr Hollande, and 22-39% will abstain. Even with a fair slice of Mr Bayrou's voters, this is not enough for Mr Sarkozy to win.

Moreover, Ms Le Pen is building a future strategy that depends on Mr Sarkozy's defeat. At an open-air May Day rally in Paris, when she announced that she would cast a “blank” ballot on May 6th, she said it was up to her voters to choose “freely”. But it is in her interest to see Mr Sarkozy lose. With an eye on the parliamentary election in June, she wants nothing less than to reshape France's political right, by turning the National Front from an extremist movement into a broader nationalist party that defends secularism, sovereignty and patriotism, has seats in parliament, and could take in refugees from Mr Sarkozy's demoralised UMP party. After the debate she declared that the election was “over” and that Mr Sarkozy would be “beaten”.

Nonetheless, in a bid for her 6.4m voters, Mr Sarkozy had been attempting to fashion a new theme: the need for more secure borders in order to “save the French way of life” and protect it from “too many” immigrants. Reminding voters of France's “Christian roots”, he took this message to towns in which Ms Le Pen had done well in the first round, such as Cernay, Alsace, where she came first, as well as to those where she did badly, such as Le Raincy, a suburb north-east of Paris, close to where the 2005 riots began. Speaking of National Front voters, he said: “I respect you, I am listening to you, and to a certain extent I understand you,” inside a municipal gym in Le Raincy filled with flag-waving supporters, many of whom had arrived from afar in hired coaches.

As tensions rose and the mud-slinging intensified ahead of May Day, a communist newspaper likened Mr Sarkozy to Marshal Pétain, France's war-time collaborationist leader. Although this is absurd, even some of Mr Sarkozy's own deputies are uncomfortable with his stridently right-wing tone. The party is divided over his strategy. Several deputies spoke out this week after Gérard Longuet, the defence minister, announced that Ms Le Pen was a possible future “interlocutor” (for his part, Mr Sarkozy has ruled out any deals with the National Front).

Despite his last-minute drive for support, and barring an eleventh-hour upset, Mr Sarkozy's days look numbered. In many ways, this is extraordinary. The man who brought freshness and dynamism to the presidency in 2007 is now facing defeat after just one term. Only one other Fifth-Republic president, Valéry Giscard d'Estaing, has failed to win re-election (in 1981). An outsider with immigrant origins, unburdened by the stale thinking of the ruling elite, Mr Sarkozy is a talented and bold politician whose election seemed to mark a turning-point: a moment when the French were ready to face up to the need for them to work more and for the state to spend less. The shame is that he proved unable in office to channel his undoubted energy in a coherent direction, or to control some of his own unfortunate impulses.

The French seem simply to have had enough of him. They are exhausted by his presidency and yearn for change. The inscrutable Mr Hollande's great fortune is that, 31 years after François Mitterrand won the first Socialist presidential victory of the Fifth Republic, he happens to embody the sort of leader for whom the French are looking right now. If, as the polls suggest, he is indeed elected, that will be the moment when his troubles begin.