French presidential candidate Francois Bayrou has almost doubled his support since saying on Wednesday he would run for office, a poll showed on Sunday, marking him out as a key figure both left and right will seek to woo in next year's election.

Bayrou, who proved surprisingly popular in the 2007 election, saw his backing jump six points to 13 percent of voter intentions in the first round of what will be a two-stage election, a LH2 poll for Yahoo showed.

The centrist politician is back in contention for third place with far-right candidate Marine Le Pen, who scored 13.5 percent of voter intentions, down 1.5 points from last month.

Bayrou, a former education minister, could take support away

not only from conservative President Nicolas Sarkozy but also from frontrunner, Socialist Francois Hollande.

At a time of loss of faith in politicians and notably traditional parties, it seems that Francois Bayrou, who says he is independent and wants national unity, has some resonance in public opinion, the pollsters said.

According to the poll, Hollande continues to lead the pack with 31.5 percent of the vote, up 1.5 percent from November 20, with Sarkozy taking 26 percent, down 3 percent.

Fifty-seven percent of those polled would back Hollande in a head-to-head contest with Sarkozy in the second round according to the survey. This was down 1 percent from November 20.

Bayrou said he would run on a national unity platform open to all reformists to prevent France's relentless decline.

Bayrou was head of the Union for French Democracy or UDF Party from 1998 to 2007, but set up his own Democratic Movement Party (MoDem) after narrowly failing to get through the first round of the 2007 election with close to 19 percent of the vote.

He became known as the Third Man with both the left and right courting him.

Pollsters LH2 said it interviewed 953 people aged 18 and over by telephone on Friday and Saturday after a European Union summit that agreed greater economic integration within the bloc.

(Reporting By John Irish; Editing by Ben Harding)