"The Normandy Times" mock-up newspaper front page features a plane and ferry leaving British shores for France, accompanied by a message urging business owners to "vote with their feet and leave post-Brexit fears behind".
The advert also includes headlines such as "20 reasons to make the move" to Normandy, and a "Hot entrepreneur wanted" classified ad extolling the virtues of the region.
But the campaign has been rejected by Transport for London (TfL), whose spokesman on Monday said it "did not fully comply with our advertising guidelines".
The Normandy campaign fell foul of TfL's rule against messages "which relate to matters of public controversy or sensitivity".
Londoners voted to stay in the European Union but were outnumbered by the national vote in 2016 and Brexit talks are currently ongoing between Britain and Brussels.
Herve Morin, president of the Normandy region, said he was surprised by such "censorship on the part of the authority in charge of the London metro, in a country which is said to be liberal".
"Our campaign has already been refused twice, so we tried to do it differently this time," said.
"We are saying to the English and to British businesses that 'there's a place for your in Normandy'," he added.
The advert will be published on Wednesday in British newspapers The Times and the Guardian, as well as The Economist weekly.
It will be followed later this month by a Normandy-branded bus which will tour the cities of Bristol, Birmingham, Cambridge and Manchester.
is due to leave the European Union on 29 March, 2019, followed by a transition period which is currently under discussion between the two sides.