LONDON, July 10 (Reuters) - Euro zone bond yields fell on Wednesday, particularly in France and Italy, in a sign of investors unwinding the political risk premium they had attached to the countries before French parliamentary elections.

The closely watched gap between French and German yields - a gauge of French risk which shot to its highest since 2012 in late June at 85 basis points (bps) - fell to its lowest since June 13 at 63.5 bps.

France's 10-year bond yield was down 9 bps at 3.169% after rising 9 bps the previous day. Yields and prices are inversely related.

Germany's 10-year bond yield, the benchmark for the euro zone bloc, fell 6 bps to 2.525% after climbing 4 bps on Tuesday.

"It's a continued correction of this sharp increase that we saw at the end of June," said Jussi Hiljanen, head of rates strategy at SEB. "Now it's normalising."

European yields, especially in France, rose at the end of June as investors worried about the threat of the French far right coming to power and driving up spending. Italian yields also climbed as investors steered away from countries with high debt levels.

Yet the election ultimately resulted in a hung parliament with the left bloc giving an unexpectedly strong showing, soothing some market nerves.

"I don't see any very strong catalyst," said Emmanouil Karimalis, rates strategist at UBS. "One day you sell off... We had (U.S. Federal Reserve chair Jerome) Powell yesterday, he didn't provide anything new but maybe his comments were on the hawkish side."

"Today we don't really have anything negative. The market is also waiting for the U.S. CPI (inflation data) tomorrow."

Traders awaited the second day of Congressional testimony from Fed Chair Powell, who on Tuesday said the central bank needed greater confidence about inflation before it cuts rates.

The key data for this week is the U.S. consumer price index (CPI) inflation data for June, due on Thursday.

Italy's 10-year yield was lower by 10 bps at 3.858%, and the gap between Italian and German yields narrowed 6 bps to 133 bps. It fell to 130 bps earlier in the session, its lowest since June 10.

Richard McGuire, head of rates strategy at Rabobank, said New Zealand's central bank signalling rates could soon fall and weak Chinese inflation data were also likely helping bonds.

Germany's two-year bond yield, which is more sensitive to European Central Bank rate expectations, was 3 bps lower at 2.901%.

(Reporting by Harry Robertson; Editing by Arun Koyyur)