It estimated that output would shrink by 0.1 percent in the last quarter, after an estimated setback of about the same amount in the third quarter.
This outlook underlines strains in the economy and comes in a week marked by a big effort by the government to reverse the falling competitiveness and a huge structural trade deficit.
The main thrust of new measures is to switch the cost of paying for social security and health benefits from employers to a wider tax base, and also to reduce public spending.
In the previous three quarters gross domestic product was flat.
These latest estimates are in line with those of the national statistics office INSEE and would mark the first recession since France was hit by the financial crisis in the first part of 2009.
A recession is considered to occur when output from one quarter to the next contracts for two quarters in a row. And emergence from recession, then a return to contraction within a few years, is commonly referred to as a double dip.
If output is flat or contracts for five quarters in a row, as the latest estimates indicate, this would be unprecedented in France since World War II.
INSEE expects the economy to have grown over the whole of 2012 by 0.2 percent, slightly less than the figure given by the government in its effort to reduce the public deficit to 4.5 percent of output at the end of the year.
Strong growth is important because it leads to higher tax revenues and to lower charges for benefits such as unemployment.
The latest estimates put France on a gloomy footing for the beginning of 2013.
The government repeated on Thursday that it is counting on the economy growing by 0.8 percent next year, but economists consider this to be optimistic. So does the European Commission which revised down its forecast for next year this week to 0.4 percent, half the government's figure.