Fears that the recovery in the 17-country eurozone has stalled were eased somewhat Monday after a survey showed business sentiment across the region rising for the first time in three months despite renewed weakness in the French economy.

The monthly purchasing managers' index for the eurozone from financial information company Markit rose to 52.1 in December from 51.7 in November. Anything above 50 indicates expansion.

The increase follows two declines and took the index close to the 27-month peak seen in September.

Chris Williamson, Markit's chief economist, says Monday the rise is a "big relief and puts the recovery back on track." The rise, he added, means that over the final quarter of the year, businesses saw their strongest growth since the first half of 2011, just before the eurozone slipped back into its longest-ever recession.

The eurozone economy has been growing for two quarters but the recovery has been unspectacular — in the third quarter the eurozone only grew by 0.1 percent from the previous three-month period, which corresponds to an annualized rate of around 0.4 percent, way down on the U.S.'s 3.6 percent.

Though Markit thinks the fourth quarter may see quarterly growth double, its headline index masks worrying developments, particularly over the state of France. Europe's second-largest economy saw its PMI fall to a seven-month low of 47.0 in December from 48.0 the previous month, with both the manufacturing and services sectors suffering.

"It's the unbalanced nature of the upturn among member states that is the most worrying," said Williamson. "France looks increasingly like the 'new sick man of Europe,' as a second successive monthly contraction may translate into another quarterly decline in GDP, pushing the country back into a technical recession."

Overall, the survey may ease the immediate pressure on the European Central Bank to do more to shore up the recovery despite below-target inflation and ongoing budget restraints in a number of economies, such as Greece, Spain and Italy.

However, with growth likely to remain modest over the months ahead, many analysts think the bank will need to do. Though the bank has little room to cut its benchmark interest rate following last month's reduction to a record low of 0.25 percent, the ECB has other potential tools at its disposal.

It could give banks more long-term, cheap loans so they can lend more. It could even decide to make banks pay to keep funds on deposit at the central bank — again, to encourage them to lend rather than hoard cash.

"Appreciable pressure remains on the bank to take further stimulative action," said Howard Archer, chief European economist at IHS Global Insight.