The estimate, which followed the Bank's forecast last month for a similar contraction in the second quarter, suggests France's 2 trillion euro economy may struggle to meet the government's forecast for 0.3 percent growth this year.
Struggling with a debt crisis and resulting budget austerity which has devastated its southern half, Europe also faces signs of stagnation and outright recession in its biggest economies.
Britain's central bank is expected to all but back off a prediction of growth for this year in a report later on Wednesday, while the latest batch of data from Germany shows both imports and exports falling.
Figures on Wednesday also showed France's trade gap widened to 5.99 billion euros in June, defying analysts' expectations for an improvement as exports of cars and transport materials slumped.
"In July, industrial activity posted a slight contraction due mainly to lower levels of activity in the automotive and textile sectors," the Bank of France said in its monthly survey. "The outlook for the coming months suggests a slight slowdown in economic activity ... GDP is expected to decline by 0.1 percent in the third quarter."
France is due to publish official preliminary data on second quarter economic growth next Tuesday.
President Francois Hollande's Socialist government has predicted the economy, which posted zero growth in the first quarter, would return to expansion in the second half of the year.
In its monthly business survey, the Bank of France said that sentiment in both the industrial and service sectors weakened to a reading of 90 in July, from 91 in June.
Purchasing managers indexes (PMIs), which gauge business activity and have a good record of tracking economic growth, showed order books at euro zone companies shriveled last month as the downturn in Germany and France became more entrenched.
source: nytimes.com
