The total figure for the 2011 deficit is now expected to be €90.8 billion ($118 billion), a drop of €4.6 billion on the last estimate.
If her prediction is right, the official figure would be lower than the most recent predictions of 5.7 percent and would signal optimism in the government's deficit cutting programme.
France hopes to reduce its deficit to 4.5 percent in 2012 and then 3 percent in 2013, with plans to balance the budget by 2016.
To reach these targets a total of €65 billion ($85 billion) of cuts and tax rises have been planned through 2015.
"These good results bear witness to the rigour, sincerity and responsiveness with which the government is managing the public finances," said the minister.
The International Monetary Fund reported some less optimistic figures about France's deficit cutting programme on Tuesday, reported business daily Les Echos.
The IMF predicts the deficit will fall to 4.8 percent in 2012 and then to 4.4 percent in 2013, higher than the 4.5 percent and 3 percent predicted by the government.
The IMF also expects growth to slow to just 0.2 percent in 2012 before increasing to 1 percent in 2013.