* FTSEurofirst 300 down 0.5 pct, falls from 6-1/2 yr high
* Shares in airlines hit by rise in oil prices
* Euronext slips again; UBS starts with 'sell' rating
PARIS, June 23 (Reuters) - European stocks fell early on Monday as downbeat readings of euro zone business activity revived worries over the pace of the economic recovery in the single currency bloc.
European airline shares fell, hurt by the rise in oil prices in the wake of the recent conflict in Iraq. Air France-KLM was down 1.9 percent and EasyJet down 2.1 percent.
At 0840 GMT, the FTSEurofirst 300 index of top European shares was down 0.5 percent at 1,388.05 points, retreating from 6-1/2 year high hit last week.
Data compiler Markit said its composite purchasing managers index (PMI) of activity in France's manufacturing and services sectors slipped deeper into contraction territory in May, dampening expectations for a rebound in the euro zone's second-biggest economy.
Separate Markit data showed manufacturing output in Germany, Europe's largest economy, increased at its weakest rate since September and service sector growth also slowed.
"The market doesn't like at all the French PMIs, and the German data is also disappointing. It eclipses the upbeat Chinese data from overnight, and it's a reminder that the latest ECB (stimulus) measures are not magic," Saxo Bank trader Andrea Tueni said.
"At these levels, investors need positive catalysts to chase stocks higher, but there aren't any. With the crisis in Iraq and the risk to see oil prices jumping, it's just tempting to book profits."
Earlier on Monday, data showed activity in China's factory sector expanded in June for the first time in six months, boosting shares in European miners such as Rio Tinto, up 2.3 percent, and BHP Billiton, up 1.6 percent.
Also bucking the trend on Monday, Spain's Dia added 3.8 percent after the world's third-largest discount supermarkets group said it had reached a preliminary deal to sell its loss-making Dia France unit to Carrefour for 600 million euros, more than what the market had expected.
Shares in European stock market operator Euronext fell 3.1 percent, adding to losses on Friday when the stock started trading following its initial public offering. The stock is down 4.8 percent from this IPO price of 20 euros a share.
UBS initiated coverage of Euronext with a 'sell' rating and a price target of 17 euros a share, citing limited upside potential for a pick-up in trading volumes in Europe.
Europe bourses in 2014: link.reuters.com/pap87v
Asset performance in 2014: link.reuters.com/gap87v
Today's European research round-up (Editing by Toby Chopra and Hugh Lawson)