* Fillon stays in presidential race despite legal probe
* Move seen strengthening position of centrist Macron
* French stocks hit 15-month high
* French/German yield gap touches tightest in a month (Adds additional named item code, no change to text)
By Dhara Ranasinghe and Danilo Masoni
LONDON, March 1 (Reuters) - The premium investors demand for holding French bonds over German ones hit a one-month low on Wednesday, while French stocks climbed to a 15-month high after French presidential candidate Francois Fillon vowed to stay in the election race.
Analysts said the move should strengthen the position of independent centrist candidate Emmanuel Macron. French bonds gyrated after a morning of speculation that Fillon was about to withdraw from the campaign over allegations of misuse of public funds, which he denies.
Fillon said on Wednesday he would remain in the French election race despite a judicial summons.
Fillon and Macron are both seen likely to beat far-right National Front leader Marine Le Pen, whichever one faces her in the May runoff, so Fillon's decision to stay in the race is reassuring, a trader at a European bank said.
Opinion polls show Macron consolidating his status as favourite.
"The word from Fillon is that he soldiers on regardless and that leaves Macron as the candidate most likely to win," said Societe Generale strategist Ciaran O'Hagan.
France's 10-year government bond yield was up just 1.2 basis points at 0.90 percent, trimming earlier rises.
That helped narrow the gap between French and German 10-year government bond yields, a barometer of how investors view relative risks, to a one-month low of 64 basis points. That is down from 84 bps last week and the widest level since late 2012.
French stocks meanwhile extended their gains after Fillon's statement, with the benchmark stock index rising 1.7 percent to around 4,944 points - the highest level since December 2015.
Shares of the biggest French banks were up more than 3 percent and were among the best performers on the blue chip CAC 40 index. Societe Generale was up 4.2 percent while BNP Paribas was up 3.9 percent.
In another twist, former agriculture minister Bruno Le Maire said he would resign from Fillon's campaign team over his vow to stay in the race despite the summons.
Fillon's campaign has been dogged since late January by an official investigation into alleged misuse of taxpayers' money involving hundreds of thousands of euros paid to his wife and family. He had been favourite to win until the affair began.
French bonds have taken a beating since the start of the year on fears about the popularity of the far right's, anti-euro Le Pen in the presidential race.
Le Pen has said she would take France out of the euro and denominate its national debt in a new currency.
But over the past week, Macron has gained ground in the polls, boosted by an alliance with centrist Francois Bayrou.
"Macron is now seen as the frontrunner to win and the most credible candidate to beat Le Pen," said Antoine Bouvet, rates strategist at Mizuho. "Fillon remaining in the race, on balance, is positive for Macron. If he had stepped down, there is no clear candidate to replace him."
The euro was down against a broadly stronger dollar, showing little immediate reaction to developments in France.
Editing by Alison Williams