Prime Minister Manuel Valls said on Saturday he is thinking about how to re-jig France's tax system to attract international firms which may be thinking of leaving London.
Sadiq Khan is working to protect City businesses' passporting rights, but many banks are considering a move should they lose their right to sell financial services in Europe after Brexit.
Speaking to Le Parisien daily, Valls said: "We know that groups based in the City are planning to leave for Dublin, Amsterdam, Frankfurt and Paris. We are working on measures that could help strengthen our attractiveness. I think notably about taxation or the status of expatriates.
"To major international companies I say: 'Welcome to Paris! Come invest in France'!"
Other destinations lining up to pocket London's big banks include Dublin and Amsterdam, but a recent poll found global institutional investors think London will remain a world-leading financial centre after Brexit.
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The French president Francois Hollande has being pressing for a speedy Brexit, saying yesterday that Britain's decision "cannot be delayed or cancelled."
Speaking at the Battle of the Somme centenary ceremonies in France yesterday, Hollande said: "Being in the European Union has its advantages and I think that is what the British people are beginning to understand, what those who are tempted by the Brexit are going to reflect upon.
"But the decision has been taken - it cannot be delayed or cancelled. Now we must take the consequences."