Yields on French long-term OAT bonds rose on Thursday at its first auction of the year as the threat of a cut to the country's AAA credit rating prompted investors to demand higher returns for buying the bonds.

Market fears about the ability of euro zone states to fund their debts remain high, and France is seen by many to be more vulnerable to contagion in the crisis than Germany.

France sold 7.96 billion euros of 10- to 30-year bonds, at the very top of its projected range, after receiving total bids for nearly 15 billion euros.

Investors demanded a yield of 3.29 percent on the 3.25 percent OAT due in October 2021, above the 3.18 percent fixed when it was last auctioned on December 1, reflecting concerns that France is on the brink of losing its triple-A credit rating.

The yield on the 4.5 percent 30-year OAT maturing in April 2041 rose to 3.97 percent from 3.94 percent in the December 1 auction, the Agence France Tresor debt management agency said.

The Treasury placed 4.02 billion and 2.165 billion euros respectively of the 3.25 percent and 4.5 percent OATs.

It also sold 690 million euros of its 4.25 percent OAT maturing in October 2023 and 1.088 billion euros of its 4.75 percent OAT due in April 2035. Those bonds were last auctioned in June 2011, and early 2010, respectively, so yields are not comparable.

(Reporting by Daniel Flynn and Catherine Bremer)