The Bank of France predicted a 0.1 percent contraction in gross domestic product (GDP) for the third quarter of this year, an outcome which, if confirmed, would follow a similar fall in output for the three months to June.
Economists define a recession as two consecutive quarters of negative growth.
France emerged from its last recession in the spring of 2009 but the economy has since struggled to gain momentum as the eurozone debt crisis weighs heavily on business and consumer confidence.
The economy was flat in the first three months of 2012 but the deteriorating outlook has forced the Socialist government to cut its growth forecast for the full year from 0.4 to 0.3 percent, and for 2013 from 1.7 to 1.2 percent.
The Bank of France's prediction for third quarter growth was based on a regular monthly economic survey.