The finding came from a Brexit design summit of leading figures from the architecture and design sector convened by Dezeen last week.
Levete, who employs 50 people in London, said the project had taken on greater significance since the Brexit vote. "Hopefully this project could be an expression of Franco-British friendship," she said.
Judy Dobias, president of London-based design PR company Camron, said that the Brexit vote had forced her company to respond by becoming more international in its outlook.
"I am staying in London but I'm going to open in Barcelona, I'm going to open in Berlin," said Dobias, who already has offices in New York and Los Angeles, and has clients across Europe.
"I think we're going to become more European," she said.
Dezeen is also considering opening an office on the continent, while French designer Nelly Ben Hayoun said she may have to relocate her business away from the UK if Brexit makes her ineligible for EU funding.
"If I cannot tap into [funding] I will have to move the company elsewhere," she said. "I'm looking into Holland or bringing it back to France."
"Having a trading arm within the EU would allow us to continue the support of our European partners," Innermost co-founder Russell Cameron told Dezeen. "Whether this is just a logistics warehouse or something greater is a decision to be made when more is known."
EOC director James O'Callaghan said the decision was not down to Brexit but added: "The Leave vote only reinforced our need for a secure foothold in Europe. Without the EU behind us, it is even more important that we establish a strong local base in Paris to service the French market, and the rest of Europe."
Speaking to Dezeen last month, Annabelle Gauberti, a lawyer who advises creative businesses, advised designers to open subsidiaries in the EU.
"EU designers could work for the subsidiaries rather than having to get visas to come to the UK," she said.
Gauberti also said creative firms should be prepared to "relocate their operations to the EU within the next two years" should Brexit result in tax and customs barriers being erected between the UK and Europe.
Several people at Dezeen's Brexit design summit called on the government to help firms get work overseas.
"It would be really great if the DTI would enable meanings and create that kind of platform for British or UK designers to have presence around the world," said architect Alison Brooks.
"Some countries, particularly Denmark and other Scandinavian countries, are fantastic at introducing their designers, setting up events and exhibitions through local embassies."
Deyan Sudjic, director of London's Design Museum, said there were concerns whether UK architects would be able to enter architectural competitions and apply for tender invitations in Europe after Brexit.
"There'll be arguments about whether you can actually as an architect take part in these competitions in Europe," he said.
Over the coming days, Dezeen will report more of the topics that emerged from our Brexit design summit and formulate ways that the design sector can help ensure the UK's departure from the EU causes minimal disruption to businesses and employees.
Yesterday we reported on the shock felt by overseas staff after last month's vote to leave the EU, with employers reinforcing the importance of making foreign workers – who make up the majority of many offices – feel that they are still welcome in the UK.