The French government is attempting to lure firms from London’s financial district ahead of the planned exit from the European Union in March 2019.
Talking of the impact of Brexit, Mr Le Maire told reporters during a visit to London: “Several thousand banking jobs will be moved to France, not several hundred.
He did not specify which banks were planning to shift jobs to the French capital but said the movement of staff and operations out of the UK will come gradually.
He said: “The shift of jobs will happen progressively and not overnight… It will be a long-term process adding that the influx of financial jobs into Paris could turn the city into a major global financial centre.”
President Emmanuel Macron’s centrist government has recently stepped up efforts to attract London banks to Paris after Britain’s divorce from the bloc by introducing incentives such as tax breaks and pledging to cut labour costs and open more English language schools for bankers’ children.
Mr Le Maire said: “It is our responsibility to make France more attractive so that more jobs can be created for the French.” He added banks would have to decide whether to leave London for Paris “alone”.
“The time when France considered finance to be its enemy is over,” he said, in a barely veiled reference to former socialist president François Hollande’s campaign claim that the world of finance was the country’s “true enemy”.
The fear of fiscal instability, he continued, is the only source of hesitation for bankers, adding that “there is also instability in Britain”.
A source close to the finance ministry said in January that the government hoped that some 3,000 jobs would be moved to the French capital by 2019.
Executives and lobbyists, however, told Reuters last month that Paris should expect see a trickle rather than a wave of City bankers arrive this year as the British government leans towards a ‘soft’ Brexit.
Earlier on Tuesday, Mr Le Maire told the BBC that “life would go on” after Brexit.
He said: “I just want to make things very clear. We want to keep a very strong positive relationship with the UK, but the British people decided to leave the EU and we have to draw the consequences.
“That does not mean we want a hard Brexit… We want a fair Brexit in the interests of the UK and of the EU.”