LONDON, Jan 4 (Reuters) - Euro zone bond yields rose sharply on Thursday after data showed inflation climbed in France and Germany in December and that the private sector downturn in the euro area was shallower than thought.

Figures on Thursday showed French inflation rose slightly in December, with the year-on-year rate at 4.1%, compared to 3.9% in November. Inflation across Germany, the bloc's largest economy, climbed to 3.8% from 2.3%, in line with expectations.

The rise in German inflation was due to base effects stemming from last December's energy relief measures for gas and district heating, the federal statistics office said.

Yields, which move inversely to prices, had been trading around 3 or 4 basis points (bps) lower in early European trading but reversed course as the data was released through the morning.

The German 10-year yield, the benchmark for the euro zone, was up as much as 12 bps at 2.14%, its highest level since Dec. 15. It hit a 1-year low of 1.896% last week.

"The wishful thinking narrative that inflation is gone and will not return, that was never true and maybe people are just coming to accept that," said Michael Weidner, co-head of global fixed income at Lazard Asset Management.

"We expect a bit of a mean reversion and that yields should rise."

France's 10-year bond yield was last 10 bps higher at 2.655%, up from an 11-month low of 2.395% touched last week.

HCOB's Composite Purchasing Managers' Index, a survey-based gauge of the euro zone's economic health, was revised up for December to match the November reading at 47.6, but remained below the 50 threshold separating growth from contraction.

Adrian Prettejohn, Europe economist at Capital Economics, said the figures did not meaningfully change the narrative around the economy and inflation.

"We expect the euro-zone economy to stagnate in the first half of the year, with only a slow recovery after that. And we think inflation will trend towards 2% by the middle of the year," he said.

Global bond yields tumbled in November and December as inflation in the U.S. and Europe slowed more than expected and central banks signalled their rate-hiking cycles were almost certainly over. That caused investors to bet on big interest rate cuts next year.

Yet yields have risen in the new year as markets have modified those rate cut bets and adopted a more cautious tone as they confront a busy economic calendar.

Traders on Thursday expected 154 bps of rate cuts from the ECB this year, down from almost 170 at the same time last week, according to money market pricing.

Germany's two-year bond yield, which is sensitive to European Central Bank interest rate expectations, was last up 10 bps at 2.511%.

The minutes from the Federal Reserve's December meeting, released on Wednesday, showed officials launched a debate on rate cuts, with some voicing fears about how long the economy can withstand the current high borrowing costs.

U.S. figures on Wednesday showed that job openings and the number of people quitting their posts fell to the lowest in around three years, although the number of Americans filing new claims for unemployment benefits fell more than expected last week, data showed on Thursday, painting a mixed picture of the labour market. (Reporting by Harry Robertson; Editing by Hugh Lawson, Barbara Lewis and Toby Chopra)