By Alun John

LONDON, July 11 (Reuters) - Euro zone bond yields dropped sharply on Thursday, mirroring a fall in Treasuries after data showed U.S. consumer inflation unexpectedly fell in June, drawing the Federal Reserve another step closer to cutting interest rates.

Germany's 10-year bond yield, the benchmark for the euro zone bloc, was down 7 basis points bps at 2.47%, having been broadly flat before the data.

The U.S. consumer price index dipped 0.1% last month after being unchanged in May, the Labor Department's Bureau of Labor Statistics said on Thursday, and rose 3.0% year on year.

Markets moved to all but price in a Federal Reserve rate cut in September after the data, adult and U.S. 10 year Treasury yields dropped around 10 bps to 4.18%.

"(Fed chair Jerome) Powell spent the past two weeks emphasizing they (the Fed) are data driven. And I'm going to take him at his word, said Kim Forrest, chief investment officer, Bokeh Capital Partners.

"Certainly, another month of this (data) gives them the ability to cut rates in the September meeting."

The European Central Bank cut its main rates by 25 basis points in June, and markets currently see two more such moves are more likely than not by year end, with around an 80% chance of another move in September.

European bonds typically react to U.S. price data both because of what it says about the inflation picture and because analysts say the ECB would not wish to diverge too substantially in policy from the Fed.

Most European bonds moved in lockstep, and France's 10-year yield was also down around 6 bps at 3.12%, leaving the gap between French and German 10 year yields at 65 bps.

That gap is a now closely watched gauge of French risk and reached its widest since 2012 in late June at 85 bps as investors feared France's parliamentary election would lead to a majority for high-spending parties, instead of the legislative gridlock that actually resulted.

Italy's 10-year yield was down 8 bps at 3.79%, its lowest since March.

Germany's two-year bond yield, which is more sensitive to European Central Bank rate expectations, was down 9 bps at 2.81%. (Reporting by Alun John Editing by Bernadette Baum and Hugh Lawson)