"The management warned us: 'If you don't sign, two sites could be closed'," an official of the FO union told AFP. Officials of two other unions confirmed the warning.
Renault, which announced last week plans to cut 7,500 jobs in France through natural attrition and early retirement, has pledged not to close any factories if unions agree to changes to improve the company's competitiveness.
Today Renault officials said "if there is not a deal it is a minimum of two sites that will close," said Dominique Chauvin of the CFE-CGC union.
Renault officials "also spoke of not making any promises on the transfer of products currently planned for France," he added.
Chauvin said the Flins plant outside Paris and Douai in northern France were likely to be targeted for closure.
Renault is seeking under the competitiveness measures a freezing of wages in 2013, a harmonisation of working hours and additional job cuts through 2016.
The company reported last week a 6.3 percent fall in its 2012 sales to 2.55 million vehicles due to an 18 percent collapse of deliveries in Europe, but said it hopes for a rebound this year.