FRANKFURT — Hopes that the euro zone could be emerging from years of torpor suffered another setback on 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 euro zone, which tracks both manufacturing and service sectors, to rise to 52, according to Barclays.

A reading above 50 is considered a sign that the euro zone 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 euro zone behind Germany’s. It would be difficult for the euro zone to grow with any vigor if France were in recession.

Over all, the survey data suggested that, even though the euro zone 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.