June 10 (Reuters) - Yield spreads between benchmark Bund and euro area government bonds widened on Monday after eurosceptic nationalists made gains in European Parliament elections on Sunday.

President Emmanuel Macron unexpectedly called a snap parliamentary election in France after his camp lost heavily to the far-right National Rally party.

The political shift may complicate European Union policymaking and attempts to deepen integration over the next five years, increasing the risk premium investors seek to hold bonds of the most indebted countries.

"The EU elections produced the expected shift to the right, but the most important development may be the severe weakening of the French and German leaders," said Citi in a research note.

"The silver lining could be an opening for Mario Draghi as European Council President and agenda setter," it added, referring to a former president of the European Central Bank.

While centre, liberal and Socialist parties were set to retain a majority in the 720-seat parliament, the vote dealt a domestic blow to the leaders of both France and Germany, raising questions about how the EU's major powers can drive policy in the bloc. It also increases uncertainty over whether European Commission President Ursula von der Leyen will be re-elected.

The yield gap between French and German bond yields - a gauge of the risk premium investors seek to hold French bonds - widened 6 basis points (bps) to 53.4 bps.

"Although other names have been mentioned, ex-ECB president Mario Draghi, Italy’s deputy prime minister Antonio Tajani or even Romanian president Klaus Johannis, von der Leyen remains the favourite, in our view," said Holger Schmieding chief economist at Berenberg, referring to the Commission presidency.

The spread between Italian and German yields – a gauge of the risk premium investors seek to hold bonds of most indebted countries – widened 8 bps to 139 bps.

The gap between Greek and German yields widened 11 bps to 105.

"As long as the centrist majority acts as a unified bloc, and the right-wing groups remain a non-coherent bloc, the impact on the course of policy will remain limited," said Marion Muehlberger, senior economist at Deutsche Bank.

"Fears of a populist shock seem to have been premature, but they may serve as a barometer of where national politics is headed," she added.

The bloc's yields edged higher on Monday as investors awaited U.S. inflation figures and the Federal Reserve's policy meeting later this week, after U.S. jobs data on Friday suggested the U.S. central bank would be in no rush to cut rates.

Germany's 10-year bond yield, the benchmark for the euro area, rose one bp to 2.60%.

Markets expect no change in Fed rates, but see a risk that policymakers' "dot plot" analysis of potential future policy changes might only point to one rate cut for this year. (Reporting by Stefano Rebaudo; Editing by Mark Potter)