Budget minister Bernard Cazeneuve said on Wednesday that 11,000 people had come forward to regularise funds hidden abroad, which could bring in one billion euros ($1.4 billion) in extra revenue.
French are coming forward to declare funds as Switzerland has curtailed its vaunted banking secrecy under international pressure and has pushed clients to report their accounts.
In June, Cazeneuve issued rules which offered lower penalties for French who came forward and reported hidden accounts, although it does not amount to an amnesty.
Cazaneuve told lawmakers on Wednesday that 11,000 people had applied to take advantage of the offer and this represents "potential revenue of more than one billion euros" for the French state.
The head of the Swiss Banking Association said in November that almost all French clients were taking up the eased regularisation measures.
Sources have said that Swiss banks are giving French clients until March to declare their accounts or have them closed.
Switzerland has agreed to an international convention against tax fraud and signed an agreement with the United States on the automatic reporting of bank account information which is expected to become the global standard to discourage tax fraud.
Early last year Cazaneuve's predecessor Jerôme Cahuzac was forced to resign after being charged with tax fraud. He was later expelled from the Socialist party.