* Investors relieved Renzi's party leads in EU vote
* French yields steady, market shrugs off National Front win
* Focus on fact pro-EU parties dominant in parliament (Updates prices, adds detail)
By Emelia Sithole-Matarise
LONDON, May 26 (Reuters) - Italian bond yields slid on Monday after Prime Minister Matteo Renzi's centre-left Democratic Party triumphed in European parliamentary elections, strengthening his mandate to push for economic reforms.
The yields were set for their biggest one-day fall since October 2013, with Renzi one of the few leaders across Europe to have scored a victory against Eurosceptic nationalists who stunned mainstream parties in France and Britain on Sunday.
Critics of the European Union more than doubled their seats in a continent-wide protest vote against austerity and unemployment but bond investors focused instead on the fact that the majority of seats would be held by parties supporting the European Union.
Renzi's party beat the anti-establishment 5-Star Movement of former comic Beppe Grillo, easing concerns that a poor result by the Democratic Party would weaken Renzi's drive for the swift reforms he promised when he took power.
Italian bonds outperformed most of the market, with 10-year yields dropping 13 basis points (bps) to 3.03 percent, while their Spanish equivalents were 7 bps lower at 2.92 percent. Traders said intra-day moves could be exaggerated by thin volumes, with British and U.S. markets closed for holidays.
"In Italy we've seen voters endorsing the policies of Renzi whose party came out as the strongest party in these elections, and this seems to be taken very positively by the market," said Christian Lenk, a fixed income strategist at DZ Bank.
"We have not seen spectacular outcomes in terms of Eurosceptic parties in the weaker countries except for Greece ... and that seems enough to draw investors back."
Greek 10-year yields were 33 bps down at 6.22 percent , reversing some of last week's rise after the anti-austerity Syriza movement won the vote but failed to deliver a knockout blow against Prime Minister Antonis Samaras's government.
A credit rating upgrade on Friday by Fitch to B from B- with a stable outlook also bolstered sentiment in Greek bonds.
French yields edged up 1 bps to 1.83 percent after the anti-euro and anti-immigration National Front's triumph, but the rise was capped as investors reckoned the result was unlikely to seriously destabilise the Socialist government.
"We doubt that the outcome will result in a marked spread widening, but the performance of French government bonds will be watched closely today with risk of underperformance," Commerzbank strategists said in a note.
With the EU vote out of the way, investors were now looking towards the European Central Bank's policy meeting next week at which it is expected to announce new stimulus measures, further supporting euro zone bonds.
Ahead of the meeting, ECB President Mario Draghi reiterated that the bank was watching exchange rate and credit dynamics carefully and stood ready to act should it see signs of a negative price spiral taking hold. (Editing by Alister Doyle and Pravin Char)