* 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 tightest in a month
* Decision Europe: Full election coverage cpurl://apps.cp./cms/?navid=72745 (Updates prices)
By Dhara Ranasinghe and Danilo Masoni
LONDON, March 1 (Reuters) - The premium investors demand for holding French over German bonds shrank to a one-month low on Wednesday, while French stocks climbed to a 15-month high after scandal-hit French presidential candidate Francois Fillon vowed to stay in the election fight.
Analysts said the move should strengthen the position of favourite Emmanuel Macron, an independent centrist candidate. 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.
Le Pen concerns many in financial markest because of her desire to pull France out of the euro zone.
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 around 2 basis points on the day at 0.91 percent, but closed the gap on German equivalents which rose 8 bps to 0.28 percent.
Euro zone bond yields rose broadly on Wednesday in keeping with U.S. equivalents as Federal Reserve officials jolted the markets into higher expectations for an interest rate hike in the world's largest economy next month.
But amid that sell-off, the gap between French and German yields, a barometer of how investors view relative risks, was the narrowest in one-month at 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 up over 2 percent at around 4,960 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 nearly 5 percent while BNP Paribas was up 4.5 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 denies wrongdoing.
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.
But over the past week, Macron has gained ground in the polls, boosted by an alliance with centrist Francois Bayrou.
The euro was down against a broadly stronger dollar, showing little immediate reaction to developments in France.
Editing by Jeremy Gaunt