The survey of activity in the private sector from purchasing managers, an important leading indicator of economic activity, came in at 48.9, up from 47.9 in July.
"August's flash PMI data signal a further drop in private sector output, although the pace of decline moderated slightly as the manufacturing downturn eased and services held its ground," Markit Senior Economist Jack Kennedy said in a statement.
The services Purchasing Managers Index rose to 50.2 from 50.0 in July, with a reading above 50 pointing to an expansion of activity.
The manufacturing PMI rose to 46.2 from 43.4 in July, a four-month high.
Markit said the survey data indicated that job losses continued in August,with the rate of decline unchanged from July.
While France avoided a contraction in gross domestic product in the second quarter, with zero growth, Kennedy said "PMI data currently suggest contraction is on the cards for" the period from July to September.
Rising unemployment would also further weaken domestic demand, he noted.