Data compiler IHS Markit said its final purchasing managers index for the manufacturing sector fell to 49.7 in March from 51.5 in February, following a preliminary reading of 49.8.
The decrease brought the index below the 50-point threshold demarcating an expansion in activity from a contraction.
In the first two months of the year, business confidence had rebounded as "yellow vest" protests against the high cost of living appeared to run out of steam.
But violence flared up again on several weekends in March, sparking clashes with police trying to stop demonstrations from descending into riots, while turnout crept up again across the country.
"Unfortunately, France's manufacturing sector could not maintain the upward momentum seen at the start of 2019," IHS Markit economist Eliot Kerr said in a statement. "As long as the 'gilets jaunes' protests remain prominent, domestic demand will be subdued and there is seemingly no support from exports."
New export business fell for the seventh month in a row in March, with demand for cars and retail products weakening, IHS Markit said.
Economists had initially been expecting manufacturing activity to remain on a par with the momentum recorded in February. Detailed PMI data are only available under licence from IHS Markit and customers need to apply for a licence.