PARIS (Reuters) - Behind on points, conservative French President Nicolas Sarkozy's last best hopes of re-election are landing a knockout punch in the sole television debate or an eleventh-hour alliance with a popular centrist.
No president in French history has come back to win after trailing as far behind his opponent in the opinion polls as Sarkozy does now to Socialist challenger Francois Hollande, political scientist Dominique Reynie said.
But veteran analysts are not writing him off just yet.
"It's hard to see what could reverse the trend, but there are a few elements," said Pascal Perrineau, director of the Centre for the Study of French Political Life (CEVIPOF) at the Sciences-Po school in Paris, citing lingering doubts among voters about whether Hollande has the stature and the national security credentials to be president.
Surveys show the conservative head of state is battling deep personal unpopularity on top of the handicaps of incumbency in an economic crisis that has seen off the leaders of 14 of the European Union's 27 countries in the last three years.
"This is at least as much a referendum on Nicolas Sarkozy as a vote in confidence in Francois Hollande," said Reynie, director of the Foundation for Political Innovation.
Yet Sarkozy is a formidable debater, and he is convinced that once he and Hollande are alone in the ring, he will be able to expose his rival's lack of government experience and fiscal credibility in a live clash a few days before the May 6 runoff.
"I'm so excited about the surprise you're going to get. You can't imagine," Sarkozy taunted reporters on a visit to Britanny on Tuesday when asked if he still believed he could win.
Among possible surprises he could spring in the final days are diplomatic initiatives on the Middle East, Africa or Europe, a move to cut petrol prices, a big order for a French industrial champion, or saving more factories from closure.
France is hosting an international foreign ministers' conference on the conflict in Syria on Thursday, featuring U.S. Secretary of State Hillary Clinton. He got the day off to an early start with calls for the establishment of humanitarian corridors to protect the Syrian opposition.
A fuel initiative seems possible after ministers confirmed that France has held talks with the United States and Britain on a possible coordinated release of strategic oil reserves to counter speculation due to tensions over Iran. But prices have already begun to fall, making that less likely.
A major contract for Airbus aircraft, made by French-based EADS EAD.PA, or for Dassault Aviation's (AVMD.PA) Rafale fighters would be a timely feather in Sarkozy's cap, but it is not clear that it would sway many voters.
India and the United Arab Emirates are both negotiating on the possible purchase of the Rafale, which France has never managed to export, despite years of intense diplomatic efforts.
A reignition of the euro zone debt crisis, already smouldering in Spain, could help Sarkozy convince voters to stick with an experienced leader rather than risking the untried Hollande.
It might also give rise to a last-minute summit with German Chancellor Angela Merkel, his closest European partner, who has kept her distance since throwing her support behind Sarkozy just before he launched his campaign in mid-February.
But it could also undermine the president's assurances that the worst of the crisis is over and that he and Merkel have "saved the euro". And officials in Sarkozy's UMP party say Merkel is no guaranteed vote-winner in France.
In politics, events can always intervene, as they did when an Islamist gunman shot dead seven people in the Toulouse region last month. That put Sarkozy in the limelight as a hands-on leader in charge of the hunt for the killer, and a consoling head of state embodying national unity at memorial ceremonies.
But attempts to build on the resulting uplift in opinion polls by staging highly publicised dawn raids on suspected Islamist militants and banning radical preachers from travelling to France failed to boost his score.
The opinion poll curves have crossed again, with most showing Hollande in front in the first round and widening his lead for the runoff.
The president's key political headache is that to clinch victory, he would need to win over first-round voters for both the far-right, Eurosceptical anti-immigration crusader Marine Le Pen and pro-European centrist Francois Bayrou.
That means doing the ideological splits.
Sarkozy has vowed to halve new immigration and battle Europe over border controls in a bid for the National Front leader's voters. Sarkozy and Le Pen have both ruled out any deal, but he is now trying hard to woo Bayrou. Some allies are urging him to offer the centrist the premiership and campaign together with him on a platform of fiscal responsibility.
"A ticket with Bayrou is his last chance, but it may be too late," said one lawmaker in the ruling UMP party, who asked not to be named.
Another disaffected former UMP politician who has drifted away from the president said Sarkozy had gambled on striking a right-wing posture and playing on fears of Islam and immigrants, but he had misunderstood the public's main concerns.
Other voices inside Sarkozy's campaign team and outside are urging him to keep to the right because Le Pen will get more votes than Bayrou, almost half of whose supporters are leaning towards Hollande, according to opinion surveys.
"If he wants to win, the big battalions are with Le Pen, so he'll have to go after them, even though he'll need Bayrou as well," said Jean-Thomas Lesueur, head of the right-leaning Paris-based Institut Thomas More think-tank.
"What could make him bounce back, if he's still able to bounce back, is if he manages to show that he has a right-wing dynamic behind him," Lesueur said.
To that end, Sarkozy has been milking public resentment of Europe by calling for the European Central Bank to do more to boost growth and picking fights with the European Commission on immigration control and trade barriers.
Polling data shows the combined left and far left vote on the first round may total up to 46-47 percent, meaning Hollande may need only a third of Bayrou's vote and a small number of Le Pen voters to put him over the top.
But the president is banking on the race starting almost from scratch in the second round, especially if he can come out even marginally ahead of Hollande on the first ballot.
Sarkozy believes he can then mobilise a "silent majority" including abstentionists, the young, women, the "white working class" and retirees in the runoff.
"There is a slight uncertainty because on the night of the first round, it will no longer be a 10-person campaign but a two-man race for the Elysee Palace," Perrineau said. "That doesn't transform the game, but there will be a slight change, and Sarkozy's image is not as catastrophic as people say."
The only TV debate considered to have swung a tight French election was in 1974, when centre-right Valery Giscard d'Estaing bested Socialist Francois Mitterrand, only to be beaten by him seven years later.
Hollande has avoided errors so far on television, coming across as calm, smiling, sometimes witty but bland, while Sarkozy has been incisive but at times irritable and aggressive in recent appearances.
"You can't rule out Nicolas Sarkozy until Nicolas Sarkozy rules himself out. Until he concedes, he's fighting," said Nicholas Dungan, a senior fellow at the Atlantic Council in Washington, who has close ties with France.
But while Hollande only needs a draw, the president needs to put the challenger on the canvas.
(Additional reporting by Catherine Bremer, Yann Le Guernigou and Tim Hepher; Writing by Paul Taylor; Editing by Will Waterman)
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