* French data brings ECB outlook back into focus
* Some in the market remain nervous about EU elections
* Rating firms may await EU polls before upgrading periphery (Updates prices, adds fresh comments)
By Marius Zaharia and Emelia Sithole-Matarise
LONDON, May 22 (Reuters) - Yields on the euro zone's lower-rated bonds stabilised on Thursday as expectations the European Central Bank will ease monetary policy overshadowed concerns about anti-austerity fallout from EU elections.
The focus moved back to the ECB after data showed French business activity contracted in May, after forecasts had called for an expansion. The German private sector's strong performance continued, but it was not enough to cause a sell-off in the bond market.
The ECB has already signalled possible monetary easing actions in June. Any weak economic data release revives the debate over whether it will start printing money to fight deflation and boost growth.
Spanish 10-year yields were 1 basis point higher on the day at 3.03 percent. Italian yields rose a similar amount to 3.22 percent.
They reversed a small dip after the French data, but remained 20 bps or more above the record lows hit last week.
The recent rise in yields followed healthy debt sales in Spain and Italy and some concern that a strong result for Eurosceptic parties in this week's European Parliament elections will weaken some governments domestically.
"Clearly we had some weak data ... and the market is now back to realising that the ECB is going to deliver something," said Jean-Francois Robin, global head of strategy at Natixis.
There was still some hesitancy to commit to big positions in the market.
Spain sold 3.53 billion euros of five- and 10-year bonds earlier in the day, the top end of the target range. Demand was weaker than it had been at previous sales but was still almost double the amount sold, giving Spain record-low borrowing costs.
"Spain remains one of the best performers in terms of fundamentals and structural reforms versus other periphery countries," said Annalisa Piazza, a market economist at Newedge.
Last week, Spain sold 5 billion euros of inflation-linked bonds and Italy sold 14.25 billion of debt. Both Spain and Italy secured about half their funding programmes for this year.
Some strategists say the EU elections could destabilise some of the euro zone governments at home.
In Greece, a strong showing by anti-bailout parties may hurt an already-fragile coalition, potentially paving the way to national elections. In Italy, a poor result for Prime Minister Matteo Renzi's party might weaken his drive for the swift reforms he promised when he took power in a party coup.
But many in the market said selling pressure was always going to be temporary as long-term investors had not participated.
"We have held substantial positions in Spanish, Italian and Portuguese bonds since the beginning of the year as we expect continued economic improvement in southern Europe," said Martin Harvey, fixed income manager at Threadneedle Investments.
"Given that the election results are unlikely to affect this backdrop, we maintain holdings through the election."
The political uncertainty may still make rating agencies cautious when they decide on Friday on the ratings of Greece, Portugal, Spain, France, the Netherlands and the UK.
"The political situation - you have to take that into account as a ratings agency," said Elwin de Groot, senior market economist at Rabobank. "It is better to wait for the outcome of EU elections and see if stability is maintained." (Editing by Jeremy Gaunt)