Banks based in London, Europe's biggest financial centre, rely on what is called an EU passport to operate across the bloc's capital market unhindered while basing most of their staff and operations outside the euro zone in London.
"If tomorrow Britain is not part of the single market, the City cannot keep this European passport, and clearing houses cannot be located in London either," Villeroy, who is also governor of the French central bank, told France Inter radio.
Paris has been a rival city to London as a financial centre.
Brexit talks will have to be quick to limit uncertainty, said Villeroy, who is also Bank of France governor.
"There is a precedent, it is the Norwegian model of European Economic Area, that would allow Britain to keep access to the single market but by committing to implement all EU rules," he said.
"It would be a bit paradoxical to leave the EU and apply all EU rules but that is one solution if Britain wants to keep access to the single market."
If that did not work out, that could be an opportunity for euro zone financial centers including Paris, Villeroy said. Some banks have said they would shift operations to the euro zone if Britain left the EU.
"It's up to us to do the right reforms to be even more attractive," he said, adding that could include tax reforms, and more incentives for expats. - Reuters
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