* Gap between French, German yields hits 78 basis points
* Jitters grow over Le Pen's pro-Frexit, anti-EU stance
* Main rivals for presidency respond to allegations
* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr (Updates with French finance minister comments)
By Abhinav Ramnarayan
LONDON, Feb 7 (Reuters) - Investor concerns that the far right could win France's presidential vote and take it out of the European Union pushed the premium investors demand to hold French government debt over German bonds to its highest since November 2012 on Tuesday.
The gap between French and German 10-year borrowing costs widened to 78 basis points in early trades as nervous investors sought safety in low-risk German government bonds.
Though the spread between the two narrowed as the session wore on, it remained near multi-year highs.
Bets against French bonds had already risen dramatically in the wake of Donald Trump's surprise win in the U.S. election in November.
These have intensified over the past two weeks as support for conservative challenger Francois Fillon has tumbled in the wake of a financial scandal. The former prime minister had been seen as a shoo-in for the Elysee palace before the scandal erupted, but opinion polls now show him crashing out in the first round.
Fillon has lost ground to independent centrist Emmanuel Macron and, more alarmingly for investors, the anti-EU National Front leader Marine Le Pen.
Le Pen promises to haul France out of the euro zone and hold a referendum on EU membership.
But while Le Pen has long been expected to reach the spring election's second round, polls show her being soundly defeated in that runoff.
As political uncertainty grows in France, the relationship between French and German bonds has weakened while that between French and lower-rated Italian debt has strengthened, suggesting French bonds are behaving more like peripheral peers.
The correlation between daily changes in 10-year bond yields in France and Germany over a 60-day period is now lower than the equivalen correlation between French and Italian yields.
The last time the correlations crossed over was early 2012 when Italian spreads widened and concerns over a euro breakup were on the rise, according to Thomson Reuters' IFR.
"The market is pricing in the tail risk of Le Pen winning the presidential elections," said DZ Bank strategist Daniel Lenz.
The phrase "tail risk" refers to an unlikely but potentially disruptive event.
French Finance Minister Michel Sapin weighed in on Tuesday, saying some investors failed to understand France's electoral system and Le Pen would not win the election.
"Those who, in good faith or by speculation, bet against France because they think Le Pen can win are not only wrong, but I'll be frank: they will lose a lot of money," he said.
While his comments chimed voter surveys, Britain's Brexit vote and Donald Trump's U.S. election win revealed the depth of of anti-establishment feeling and highlighted the unreliability of opinion polls.
BlackRock's global chief investment strategist, Richard Turnill, said in a note that he believed the risk priced into European markets around this year's French and German elections was overstated.
Such sentiment helped push yields lower as the session wore on, with France's 10-year bond yield down 4 basis points on the day at 1.10 percent, and the gap to German equivalents narrowing to 73 bps.
"There is always the conflict between fear and greed," said Commerzbank strategist David Schnautz. "I guess fear pushed the yields so high that some investors could not resist."
The cost of insuring against volatility in the euro versus the dollar over the next three months rose to its highest in over a week on Tuesday as contracts took in the date of the final round of France's presidential vote.
French stocks underperformed the pan-European STOXX 600 index, though traders ascribed this to a fall in banking shares after BNP Paribas shares reported sub-forecast fourth-quarter profits and its shares fell 4 percent.
Doubts over a rescue package for Greece were also stoking concerns over the future stability of the euro zone.
Greece's two-year bond yield topped 10 percent for the first time since June on growing worries over whether the European Union and the International Monetary Fund can reach an agreement over a third Greek bailout. (Additional reporting by Vikram Subhedar and Dhara Ranasinghe and Michel Rose in Paris; Editing by Richard Lough)