UPDATE 1-French borrowing costs drop in first test since downgrade

* 15-year bond sold at record low yield at auction

* Bond rally eases pressure on Hollande over economy

* 10-year benchmark bond under 2 pct for first ever

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PARIS, Dec 6 (Reuters) - France's long-term borrowing costs hit a record low at an auction on Thursday as investors favoured the relative safety of French paper despite last month's Moody's downgrade and concerns over flagging competitiveness.

France's debt management agency, Agence France Tresor, reported strong demand at the first auction of long-term debt since last month's one-notch downgrade, with three times as many bids as bonds sold.

The rally in French bonds comes despite widespread doubts over whether President Francois Hollande's government will be able to keep its deficit-cutting promises next year as France's 2-trillion-euro economy remains in the doldrums.

With data on Thursday showing unemployment hit a 13-year high of 10.3 percent in the third quarter, France's low borrowing costs are a rare piece of goods news for Hollande's Socialist government.

"French debt has remained relatively solid versus its EMU (euro zone) peers despite ... the downgrade by Moody's and risks for economic activity heading into 2013," Newedge Strategy market economist Annalisa Piazza said.

Investors snapped up the 6-, 7- and 15-year bonds at lower yields than the last time they were auctioned with the longest-term bond being sold at an all-time low of only 2.56 percent.

Though the national debt is flirting with an unprecedented 90 percent of output, France has been borrowing this year at record lows as investors seek out the relative safety and high liquidity of its large bond market.

The benchmark 10-year bond fell below 2 percent on Wednesday for the first time despite Moody's downgrade, which followed in the footsteps of a similar move by Standard and Poor's at the beginning of the year.

France has sold short-term debt at negative yields this year, meaning investors are paying to park cash in the safety of French bills.

DEFICIT TARGETS UNDER PRESSURE

The falling yields come despite concerns over France's failure to reform its economy and make it more competitive.

French debt, about 50 percent of which is regularly bought by central banks and sovereign wealth funds, has benefited from record buying from Asia and the Middle East as investors seek out richer yields than those on German bonds.

"Although we suspect France will not be a strong performer amongst the EMU core countries in 2013, we would not be too pessimistic as 2012 was a relatively good year for the French debt despite all the negative news," Piazza said.

Determined to forge its fiscal credibility, Hollande's government aims to carry out an unprecedented belt-tightening effort next year and cut the public deficit to 3 percent of national output from an estimated 4.5 percent in 2012.

However, many economists say that growth will fall short of the government forecast of 0.8 percent next year, putting the deficit target out of reach.

AFT said it sold 3.97 billion euros of long-term bonds, known as OATs. That was at the top of its projected target of 3-4 billion euros for its last bond auction of 2012.

AFT, which has already begun raising funds for 2013, said the average yield on the October 2018 OAT fell to 1.01 from 1.29 percent at the last auction in October.

The average yield on the October 2019 OAT slipped to 1.27 percent from 2.02 percent at its last auction in July.

The October 2027 OAT saw its yield decline to 2.25 percent from 2.85 percent at the last auction in September.

(Additional reporting by Alexandria Sage and Emelia Sithole-Matarise in London)