Michel Sapin told Sky News on Friday:
"There will be consequences [to Brexit]. But one thing is sure, no one in the Eurozone will accept that the main clearing place will be outside the European union.
"So there will be activities that are taking place in London that will only be able to take place on the territory of the European union.
"And from that point of view Paris is extremely well placed taking into consideration its current capacities to carry out these activities."
Clearing houses in London manage credit risk, acting as a middle-man in swaps and derivatives trades to guarantee the contract in the event that one of the parties involved in the trade goes bust.
The acceptance of English law and widespread use of English language has made London a hub for clearing globally. It controls 70% of clearing involving euro-based deals, according to Sky News. Bloomberg says London processes $570 billion (£460.9 billion, €511 billion) worth of trades daily.
Britain repeatedly had to defend its right to clear trades, given that it does not have the euro. The UK last year won a court battle to continue clearing in London.
However, France has repeatedly signaled that it wants to steal the business from London. Sapin's comments echo those of President Francois Hollande, who said Britain couldn't retain its key clearing role shortly after the June 23 referendum. France has also tried to lure British finance firms to Paris, promising to fast-track regulation applications. Paris, London's nearest rival for clearing, handles 11% of all euro trades.
Chancellor Philip Hammond told Bloomberg in New York on Thursday: "It's by no means clear to me that the rules of the single market, even after Britain has left, would permit the ECB to require euro-denominated instruments to be cleared inside the euro zone."
Sapin's comments come as Hollande said in a speech that Europe must have "a threat, a risk, a price," to bring to the table during Brexit negotiations with the UK. The comments have sent the pound diving yet again against the dollar and euro.