Time is running out for Nicolas Sarkozy. France goes to the polls on Sunday in the first round of presidential elections, and the incumbent has failed to turn around a long series of opinion polls that show him losing to Socialist challenger François Hollande.

Whether Sarkozy or Hollande leads coming out of the first round is not particularly important — they are both well clear of their rivals, so there is no doubt that they will face off in the second round (to be held two weeks later, on May 6). At the moment they seem almost neck and neck, with Hollande perhaps slightly in the lead. But in the run-off, which is what matters, Hollande has maintained a clear advantage, consistently polling between 53% and 57%.

If Sarkozy can manage to get his nose ahead in the first round that would give him a slight morale boost, but not enough on its own to change anything. The real importance of the first round is twofold: it will tell us if there’s something that the polls are not picking up, and what the breakdown of the vote is among the also-ran candidates.

French opinion polls have a pretty good record (Wikipedia has a comprehensive summary of this year’s), and you can compare that with how they performed in 2007). The major mistake they made last time was in overstating the vote of the far-right National Front candidate, Jean-Marie Le Pen, who had been polling over 13% but managed only 10.8% — the exact opposite of the error one expects with polling for extremist candidates.

There are 10 candidates on the ballot on Sunday, but only three in addition to the two front-runners that look like getting more than 1% or 2%: Marine Le Pen for the National Front, Jean-Luc Mélenchon of the Left Front, and François Bayrou of the centrist Democratic Movement. Le Pen and Mélenchon have both been polling in the mid-teens, with Bayrou in fifth place on around 10%.

Although Bayrou’s support is well down from 2007, when he managed 18.6%, his votes are possibly the most important. National Front and Left Front votes will flow strongly to Sarkozy and Hollande, respectively, in the second round (although more so on the left, which is one of Sarkozy’s problems). But Bayrou’s are something of a wild card; the most recent TNS-Sofres poll shows 43% of the centrist vote going to Hollande, 33% to Sarkozy and 24% abstaining or undecided.

So Bayrou is in the reverse position to where he was in 2007. Then it was the Socialist candidate Ségolène Royal who trailed in the polls and desperately needed his endorsement; in return she promised to make him prime minister if she won. But Bayrou stayed neutral, and Sarkozy duly prevailed with 53.1% in the second round.

This time it’s Sarkozy who needs all the help he can get. Le Monde wonders today, “On the evening of 22 April, will Nicolas Sarkozy pick up his telephone? Will the two men talk to each other?” Support from Bayrou seems the one thing that just might shake up the race enough for Sarkozy to draw ahead. But there is a lot of bad blood between them, and it seems much more likely that Bayrou will stay out of it and take his chances with a Hollande presidency.

Nor is Bayrou the only old foe coming back to haunt Sarkozy. Persistent reports claim that his predecessor, Jacques Chirac, and his entourage are covertly supporting Hollande. After 12 years in office, Chirac five years ago was deeply unpopular, but now he is apparently “polled as one of France’s best-loved political figures”.

Maybe five years out of office will do the same to Sarkozy’s reputation.

At this stage it certainly looks as if he’ll get the chance to find out.