LONDON, July 5 (Reuters) - Euro zone bond yields fell slightly on Friday morning as traders waited for key U.S. jobs data later in the day, while also weighing up a landslide Labour victory in Britain's general election.

Germany's 10-year bond yield, the benchmark for the euro zone bloc, fell 2 basis points (bps) to 2.562%. Yields move inversely to prices.

French and Italian bond yields fell further, keeping up the recent trend of a decline in the risk premiums investors demand to hold those countries' bonds.

A

poll

on Wednesday showed Marine Le Pen's far-right Rassemblement National party is likely to fall short of a majority in Sunday's French parliamentary election, soothing

investor nerves

about the party's potential spending plans.

France's 10-year bond yield was down 3 bps at 3.245%, set to end the week around 4 bps lower.

The gap between French and German 10-year borrowing costs - a gauge of French risk - fell to its lowest since June 13 at 67.6 bps and was last at 68.6 bps.

"The French election outcome is unlikely to stir markets as tail risks have faded," said Benjamin Schroeder, senior rates strategist at ING.

Italy's 10-year yield was lower by 6 bps at 3.95%. The gap between Italian and German bond yields narrowed to 139 bps, around the lowest since June 13.

Markets showed little discernible reaction to Britain's general election, where Keir Starmer's Labour party swept to a landslide victory.

UK bond yields were down around 4 bps, broadly in line with European markets. The

pound and UK stocks

rose after the result.

The focus was on monthly U.S. jobs data, due out at 1230 GMT (8.30 a.m. ET), which is expected to show employment and wage growth cooled in June.

A string of weaker U.S. economic figures, including a big drop in a survey-based gauge of the

services sector

, has bolstered investor hopes that the Federal Reserve will cut rates this year and helped bond yields cool around the world.

"Soft data keeps pointing at a weakening labor market," Schroeder said. "A consensus reading or lower would help build a Fed cutting narrative for September, helping both U.S. and euro rates to fall."

Germany's two-year bond yield, which is more sensitive to European Central Bank rate expectations, was down 1 bp at 2.929%. (Reporting by Harry Robertson; Editing by Andrew Heavens and Anil D'Silva)