The latest estimate from the Bank of France differs from data from the national statistics office INSEE which has suggested that France, which has the second-biggest eurozone economy, just averted recession this year with marginal intermittent growth.
Together, the sets of data suggest that the country is bumping along on the edge of recession when it urgently needs to achieve steady, stronger growth to generate activity, reduce high unemployment and raise tax revenues to reduce the public deficit.
The Socialist government switched the emphasis of its economic policy a few months after coming to power in May, focusing on the need to raise the competitive position of French industry to boost exports and correct a big trade deficit.
The central bank stood by its view that the country fell into mild recession on the basis of its latest monthly report in December on the state of activity in the industrial and services sector.
The bank's overall assessment of how the economy fared in the fourth quarter was the same as those it issued in November and October.
The bank had already said it believes the economy shrank by 0.1 percent in the third quarter from the previous three-month period.
The technical definition of recession is two quarters running of contracting output.
However, INSEE estimates that the economy grew by 0.1 percent in the three months from July to September, keeping France out of recession.
INSEE believes that the economy then contracted by 0.2 percent in the final quarter of the year.
Meanwhile, INSEE reported on Thursday that French industrial output had rallied by 0.5 percent in November from the level in October, when it contracted by a revised 0.6 percent on a monthly basis.
The statistics institute had estimated initially that industrial output had shrunk by 0.7 percent in October.
Analysts at BNP Paribas commented however that "this unexpected rise is fragile," and noted that industrial production was still down by almost 4.0 percent on an annualized basis
They nonetheless forecast that the French economy might have reached its trough at the end of last year, noting that "confidence indices in November and December point towards a timid improvement in the coming months."
Meanwhile, INSEE said that consumer prices had risen by 0.3 percent in December and by 1.2 percent, excluding the price of tobacco, on a 12-month basis.
The increase had been driven mainly by seasonal increases in the prices of services and manufactured products, data showed.
The latest figure means that inflation in France was below the average of 2.2 percent in the eurozone in December, on the basis of a first estimate by the European Union statistics office Eurostat.
BNP Paribas analysts noted that was "a positive point for consumers and French competitiveness."