* Macron's party set for huge French parliamentary majority
* Italy's 5-Star suffers sharp setback in local vote
* French, Italian spread vs German tightens sharply
* Italian, Portuguese, French yields at new lows
* Euro zone periphery govt bond yields http://tmsnrt.rs/2ii2Bqr (Updates prices)
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.
But 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 slid 8 basis points to 2.01 percent, the lowest since January. 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 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.
Stability in France also contrasts with Britain, where the ruling Conservative party lost its parliamentary majority last week, just days before negotiations over the UK's departure from the EU begin.
"While the political situation in the UK has become more complicated, across the Channel, conventional wisdom appears to have been turned on its head as Macron's new party ... has swept the board in the first round of French parliamentary elections, no mean feat for a movement that didnt even exist two years ago," said CMC Markets chief market analyst Michael Hewson.
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(Editing by Catherine Evans)