"Large international banks... have already undertaken real due diligences and we have received a lot of practical questions regarding the way they are going to be managed from our perspective, with their relationship with the French regulators," Benoit de Juvigny, secretary general at the AMF, said in an interview with BBC television late Wednesday.
Britain's powerful banking lobby has warned that international lenders with operations in the UK are ready to transfer some of their activities out of the country from early 2017.
Big banks have publicly voiced their fears about the impact of Brexit, including potential loss of access to the European single market.
"Of course London has great expertise but don't underestimate our expertise," said de Juvigny, adding that he sees the prospect of regulating banks wishing to move to Paris as "a welcome challenge".
"Also it is a dangerous challenge because we could see some kind of new competition between countries, between regulators," he said.
Conservative Prime Minister Theresa May has stated that she will formally trigger the two-year EU divorce process by the end of March 2017.
However, Brussels and London face the daunting prospect of gruelling negotiations on future trade deals with the European Union and countries outside of the bloc.
EU "passporting" rights currently allow financial products approved by a single regulator in a member state to be sold in the entire European Union.
But firms registered in the UK risk losing this access when Britain leaves the bloc, which could push some companies to move at least some of their activities to continental Europe.