June 21 (Reuters) - German government bond yields fell on Friday after economic survey data for the euro zone came in weaker than expected, supporting expectations for policy rate cuts.

Euro zone yields bounced around in the afternoon session in Europe, as traders digested U.S. data showing a pick-up in business activity and remained nervous about political uncertainty in France.

Euro area business growth decelerated sharply this month as demand fell for the first time since February, survey-based data showed on Friday.

Weak demand dragged down France's business activity as the country heads into a snap parliamentary election, while an upturn in Germany slowed in June.

German 10-year bond yields, the benchmark for the euro area, fell 3 basis points to 2.399%.

French 10-year yields, fell in morning trading before reversing course later in the day to trade roughly flat at 3.156%.

The gap between French and German 10-year yields - a gauge of risk premium investors demand to hold French government bonds – widened 3 bps to 75 bps, having gapped to around 80 bps last Friday, its widest level since February 2017.

Surveys "suggest a solid recovery in the euro zone economy is not a done deal", said Franziska Palmas, senior European economist at Capital Economics.

"Meanwhile, aggregate price pressures continued to ease but remained strong in the services sector, which will keep ECB policymakers cautious," she added.

Money markets price in around 70 bps of cumulative European Central Bank rate cuts by year-end from 65 bps before PMI data, implying a further move and a 70% chance of a third cut in 2024.

Bund yields were on track for a 4-bp weekly rise, as hopes that France's far right National Rally (RN) party will backtrack on fiscally expensive pledges stopped last week's rush into safe-haven assets.

"OATs (French government bonds) look priced for a hung parliament/RN-lead with a benign fiscal outcome but might widen sharply to 100 bps over Bunds on a more forceful far-right/left manifesto implementation, while tightening to 60 bps on a centrist coalition," Citi analysts said.

RN is seen leading the first round of the country's parliamentary elections with 35% of the votes, according to a survey released on Thursday. President Emmanuel Macron's centrist camp was in third place with 20% of the votes.

Market sentiment towards France and the euro area's most indebted countries improved on Thursday as the market got through a French bond auction largely unscathed.

There were also hopes of monetary easing ahead after the Swiss National Bank marginally surprised markets by cutting rates, and the Bank of England delivered a dovish message, analysts said.

Italy's 10-year yield was down 1 bp at 3.931%, while the Italian-German yield gap stood slightly wider at 153 bps. (Reporting by Stefano Rebaudo, additional reporting by Harry Robertson, editing by Alex Richardson and Emelia Sithole-Matarise)