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FRANKFURT, Germany — Hopes that the eurozone could be emerging from years of torpor suffered another setback Thursday when an indicator of economic activity in the region slipped unexpectedly and suggested that France could be sliding back into recession.

The indicator, a survey of purchasing managers published by the research firm Markit, fell to 51.5 in November from 51.9 in October, according to preliminary data, as the decline in France offset further improvement in Germany. Economists had expected the composite index for the eurozone, which tracks both manufacturing and service sectors, to rise to 52, according to Barclays.

A reading above 50 is considered a sign that the eurozone economy is growing. But the index for France fell to 48.5 in November from 50.5 in October, the latest sign of shrinkage in the French economy, the second-largest in the eurozone behind Germany’s. It would be difficult for the eurozone to grow with any vigor if France were in recession.

Overall, the survey data suggested that, even though the eurozone as a whole pulled out of recession in the second quarter of this year, the recovery lacks momentum and is vulnerable to shocks, such as a sag in demand from China and other emerging markets.

“Any improvements were largely confined to Germany,” said Chris Williamson, chief economist at Markit. “France, on the other hand, showed further signs of being the ‘sick man of Europe.’”