The rate of decline eased following an improvement in the performance of the service sector, Markit said, which moved into expansionary territory. The country's manufacturing sector, however, disappointed, shrinking further in July.
The data come after economic growth in France ground to a halt in the first quarter. Gross domestic product (GDP) for the country was flat in the first three months of the year, after posting 0.2 percent growth in the fourth quarter of 2013.
Jack Kennedy, senior economist at Markit, said the PMI data indicated the country's economy was showing "little sign of turning around its recent sluggish performance."
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In a note following the release, Naeem Aslam, chief market analyst at AvaTrade, added: "The fact remains very clear that growth story in the biggest economy of the Europe is not as robust as it was and the question stands that how long investors can turn their blind eye to this."
Germany's economy 're-accelerated'
It was a different story in Germany, however, where the flash composite PMI came in at 55.9 in July, up from 54.0 in June.
The services sector drove this acceleration in growth, Markit said, with activity growth hitting a 37-month high. Here - unlike in France - manufacturing output also rose.
"Following the joy of lifting the football World Cup trophy, July's flash PMI results provide further positive news for Germany," Oliver Kolodseike, an economist at Markit, said in a note.
"The headline index - which measures the combined output of both the manufacturing and services sectors - rose to a three-month high at the start of the third sector, suggesting that growth in the euro zone's largest economy has re-accelerated."