But Mr Bayrou is playing hard to get, choosing this week to endorse neither.
The candidates have their eyes firmly pinned on Mr Bayrou's first-round vote of 18.6%.
If the centrist Mr Bayrou decides to endorse one of the two candidates, this could help.
ECONOMIST: Nicolas Sarkozy and S��gol��ne Royal make the run-off
Down on a farm in the Loire valley, Bayrou is stressing his rural roots.
Speaking on French radio Europe 1 Friday, Sarkozy questioned the logic of Bayrou's decision to back Hollande.
CNN: French presidential rivals enter final day of campaigning
Mr Bayrou scraped 7% in 2002, but he has been quietly gaining ground: one Ifop poll gave him 12%.
Mr Bayrou's new Democratic Movement (MoDem) looks somewhat isolated with only three seats.
Those far-right views do not fit with the values of his MoDem (Democratic Movement) party, Bayrou told reporters in Paris Thursday.
CNN: French presidential rivals enter final day of campaigning
Mr Bayrou wants an all-embracing new centre party to outflank the Front.
Nicolas Sarkozy's share of the national vote has dropped from 31% to 27.2% on Sunday, and Francois Bayrou's by more than half to 9.1%.
Mr Sarkozy told a philosophy magazine recently that paedophilia and suicidal tendencies were probably genetic traits, provoking sharp criticism from Ms Royal and Mr Bayrou.
Despite the emergence of the centrist contender Francois Bayrou as a third force at the presidential election, the parliamentary vote largely confirmed the two-party system.
I'm not sure if Mr Bayrou has a realistic chance of being elected, to be honest, but with so many French voters still undecided, nothing is certain at this stage.
Mr Sarkozy will be squeezed in the centre by Mr Bayrou, who emerges from nowhere to fight each presidential poll, and on the far right by a revived Ms Le Pen.
He said that he had heard the call by supporters of Marine Le Pen for "the nation, borders, authenticity, authority, firmness", and that he shared centrist Francois Bayrou's concern to reduce the deficit.
Bayrou accused Sarkozy of lurching to the extreme right in the past two weeks of campaigning, as he attempts to appeal to the 6.5 million first-round supporters of the far-right National Front party, BFM-TV reported.
CNN: French presidential rivals enter final day of campaigning
Centrist Francois Bayrou, who took 9% of the first round vote, delivered a boost to Hollande's campaign Thursday when he said he would vote for the Socialist, and urged his supporters to vote according to their conscience.
CNN: French presidential rivals enter final day of campaigning
Mr Bayrou also comes from a farming background, so he understands the different interests of rural and urban voters, which is important to me as someone who lives in Brittany, but has also previously lived in Paris.
She will now need to convince voters in the centre, as well as fellow Socialist Party members from the social-democratic wing who had urged her to team up with Mr Bayrou, that she can speak to them too.
ECONOMIST: Nicolas Sarkozy and S��gol��ne Royal make the run-off
So the Gaullists, temporarily led by the young and ambitious Nicolas Sarkozy, the party's secretary-general, find themselves squeezed between Mr Pasqua's Europhobes, currently attracting 10-12% of the vote, and Mr Bayrou's Euro-federalists with 8-9%, leaving the main Gaullist-Liberal Democratic list with a wretched 17-20%.
应用推荐