PARIS — The euro zone economy expanded in June for a 12th straight month, a private sector report indicated on Monday, but the pace of growth slowed and there were signs that the French economy may again be shrinking.

A broad index of economic output based on surveys of purchasing managers by Markit Economics, a data analysis firm based in London, came in at 52.8 in June, down from the 53.5 recorded in May and falling to the weakest pace since December.

A number above 50 indicates expansion, while a number below that level suggests contraction. Economists see the surveys as providing one of the most timely indicators of the state of the euro zone economy.

The data showed a glaring discrepancy between most of the currency bloc and France, where a broad-based slowdown appears to be underway, Markit said. Businesses are shedding more workers at a time of already high unemployment.