Calais regional president Xavier Bertrand said it was not France”s job to police the border of a country not in the European Union.
Speaking on radio today, he said: “If Britain leaves Europe, right away the border will leave Calais and go to Dover.
“We will not continue to guard the border for Britain if it”s no longer in the European Union.”
Under the terms of the Le Touquet Treaty, British border checks currently take place on the French side of the Channel.
But French officials have long complained that the burden of policing the border is much heavier for France than for the UK because far more migrants are trying to enter Britain illegally than the other way around.
There are currently around 5,000 migrants sleeping rough in Calais, where a court is set to decide this week on whether to bulldoze half of their makeshift camp known as the Jungle.
Belgium has just re-established border controls in fear that, if the camp is demolished, the migrants may leave France looking for an easier route to the UK.
Mr Bertrand also recently accused the UK of “social dumping” by failing to take responsibility for the Calais migrants.
He told a French newspaper: “Mr Cameron is not taking this issue seriously. His latest actions have been too little too late.
“If his inaction continues, we should let the migrants cross the Channel and he can deal with them in his own way, on his own island.”
He added: “The English need to change their labour laws for migrants because even if in theory you need some paperwork to work, it”s possible to work on the black market and lots of employers exploit this for cheap labour.
“You English must stop your social dumping and get your labour laws in order.
“You have to act, or we must move the border back to Dover where it belongs.”
Calais mayor Natacha Bouchart also recently blamed Britain”s “black market economy” and “cushy benefits system” for the illegal immigrant crisis in her town.
She said the UK should be forced to abandon border checks for travellers arriving from Europe to help move the migrants away.
Ms Bouchart said: “They want to go to England because they can expect better conditions on arrival there than anywhere else in Europe or even internationally.
“There are no ID cards. They can easily find work outside the formal economy, which is not really controlled.
“Calais is a hostage to the British. The migrants come here to get to Britain.
“The situation here is barely manageable. The UK border should be moved from Calais to the English side of the Channel because we”re not here to do their jobs.”