The central bank previously expected growth to be essentially flat in the three months from April through June. If the figures are confirmed it would be the first quarterly contraction since France pulled out of recession in 2009.
A second contraction in the third quarter would mean that France joined other EU countries like Britain, Greece, Italy, Portugal and Spain in recession.
In its latest outlook, the national statistics office INSEE forecast second quarter economic growth of 0.2 percent, but the figure was issued in March and several indicators released since then suggest it could be revised lower.
The French customs service reported meanwhile on Friday that the national trade deficit deteriorated in April to €5.8 billion ($7.3 billion).
But the public deficit declined by €1.5 billion in April from the same month a year earlier, owing to increased tax revenues and a one-off boost from the sale of fourth-generation telephone frequencies, the budget ministry said.
France managed to reduce its public deficit to €59.9 billion, which "at this point in the year" was in line with a 2012 budget established by the former conservative government, a ministry statement said.
On May 15, INSEE said the French economy had stalled in the first quarter of 2012.
In addition to recording zero growth in the first three months of the year, INSEE revised its fourth quarter 2011 growth figure down to 0.1 percent from 0.2 percent, but maintained that output had expanded by 1.7 percent in 2011.
Meanwhile, French unemployment climbed higher in the first quarter of 2012, hitting the symbolic level of 10 percent, up by two percent from the previous three-month period INSEE said Thursday.
That put the French unemployment rate back to a level last seen in 1999.
The European Commission has forecast overall growth this year of 0.5 percent in France, in line with budget predictions by the new Socialist French President Francois Hollande.
But the Commission expects growth next year of 1.3 percent, against a forecast of 1.7 percent under Hollande's economic programme.
In April, France's trade deficit was €200 million bigger than in March, and reached a total of €5.8 billion, the customs service said Friday.
"Exports are generally well oriented, but suffered from hits in the aeronautic sector and a decline in sales of refined petroleum products," the service said in a statement.
"Imports are underpinned by large purchases of energy products, intermediate and capital goods," it added in reference to products often used to manufacture consumer goods and other finished items.