* Euro zone periphery govt bond yields tmsnrt.rs/2ii2Bqr (Adds economist comment, background, updates prices) LONDON, June 28 (Reuters) - Euro zone bond yields fell on Monday, with news that France’s far right failed to win a single region in weekend elections bringing some relief to French bond investors. Sunday’s vote in the southern Provence-Alpes-Cote d’Azur had been seen as the far right Rassemblement National (RN) party’s best opportunity to secure its first ever regional power base, but other parties united to keep it out. The results, while depriving RN leader Marine Le Pen of a chance to show her party is fit for power ahead of next year’s presidential election, also showed no wins for the party of French President Emmanuel Macron. France’s 10-year bond yield fell 4 basis points to 0.16% , with the gap over German Bund yields tightening a touch to 34 basis points (bps). “I do see a small tightening of French bonds versus Germany this morning, nothing out of the ordinary,” said ING senior rates strategist Antoine Bouvet. He said one reason could be that the results confirmed a poor showing for the far right hinted at in the first round, and that “decent results” for the centre right Les Républicains suggested a three - rather than two - horse race at next April’s presidential election. “This could mean two centrists making it to the run off, or this could mean a further splitting of centrist votes that would favour Le Pen,” Bouvet said. “I am tempted to lean towards the more optimistic interpretation but it is hard to draw firm conclusions, and the lack of market reaction suggests that I’m not the only one.” “The outcome of the French 2022 elections seems even more open than before the regional vote,” Holger Schmieding, an economist at Berenberg, said. Most 10-year bond yields were lower as investors looked ahead to this week’s flash euro zone inflation numbers and the U.S. non-farm payrolls report. Meanwhile, some of them had been increasingly concerned about a possible new wave of the pandemic after the summer as the Delta variant continued to spread. Germany’s benchmark 10-year Bund yield was 3 basis point lower at around -0.19%. Jacob Nell, head of European economics at Morgan Stanley, said he expected a slow grind higher in bond yields, led by U.S. Treasuries. “In Europe, where we see lower inflation a dovish ECB (European Central Bank) that continues to buy bonds, yields will follow the U.S. higher to a lesser degree,” he said. A hefty week for bond supply could put some upward pressure on bond yields. According to ING, more than 30 billion euros ($36 billion)of scheduled supply is possible from Belgium, Italy, Spain and France. Analysts said the highlight was further issuance from the European Union to fund the bloc’s recovery fund. ($1 = 0.8376 euro) Reporting by Dhara Ranasinghe, additional reporting by Stefano Rebaudo; Editing by Jonathan Oatis Our Standards: The Thomson Reuters Trust Principles.