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* Macron's party set for huge French parliamentary majority
* Italy's 5-Star suffers sharp setback in local vote
* Italian yields below 2 percent, French yields at new low
* Finnish bonds underperform as government falters
* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr (Updates prices)
By Dhara Ranasinghe
LONDON, June 12 (Reuters) - Prospects of victory for French President Emmanuel Macron's fledgling party and a setback for Italy's populist 5-Star Movement soothed political worries in euro zone debt markets on Monday, sending yields to multi-month lows.
Projections from the first round of Sunday's French parliamentary election suggested Macron's LREM party was set to secure a big majority to push through pro-business reforms.
Meanwhile, Italy's 5-Star Movement looked likely to suffer a severe setback in local elections, a development that could undermine its hopes of winning a national vote due by May 2018 and which suggests it is losing steam like other anti-establishment parties across Europe.
Those signs of stability and cohesion in two of the euro zone's biggest economies were viewed as positive not just for French assets, but also for peripheral markets that have been in the firing line from any signs of instability in the bloc.
That comes on top of stronger economic growth and indications that the European Central Bank is in no rush to withdraw its massive monetary stimulus. "Confidence in the euro zone is building and political risks are fading," said RBC's global macro strategist Peter Schaffrik.
"The data is strong and the ECB is keeping monetary policy loose, so we have this Goldilocks scenario for bond markets."
Italian 10-year government bond yields fell below 2 percent for the first time since late January, down 9 basis points on the day. That pushed the gap over German peers to around 175 basis points -- its narrowest since late May and down almost 30 bps from Wednesday.
Italian yields ended Friday with their biggest weekly fall of 2017 as a failure to reach an agreement on a new electoral law was seen reducing the chances of early national elections.
Portugal's 10-year bond yield hit a nine-month low at 2.97 percent on Monday, while Spanish peers fell to 1.39 percent -- their lowest level since January.
The euro firmed against the dollar, while euro zone shares were broadly weaker.
French bonds outperformed higher-rated euro zone equivalents, with 10-year yields falling 5 bps to a seven-month low of just under 0.60 percent.
That left the gap over Bund yields at around 35 bps versus 39 bps on Friday.
Pollsters project Macron's alliance could win as many as three-quarters of the seats in the lower house after next week's second round of voting, giving Macron a powerful mandate.
Rating agency S&P Global Ratings said on Monday it was likely to raise its growth outlook for France and the euro zone now that Macron looks poised to win a huge majority.
Elsewhere, Finland's bonds underperformed euro zone peers as its Prime Minister moved to break up its three-party coalition, saying he wanted to eject the nationalist Finns Party days after it chose a new anti-immigration leader.
For Reuters Live Markets blog on European and UK stock markets see reuters://realtime/verb=Open/url=http://emea1.apps.cp.extranet.thomsonreuters.biz/cms/?pageId=livemarkets
Additional reporting by John Geddie; Editing by Catherine Evans