Xavier Bertrand told the BBC broadcaster that migrants should be allowed to apply for asylum at "hotspots" in France instead of waiting for a possibility to reach Britain to do so.
Most of the refugees and migrants in the Calais camp come from conflict zones like Afghanistan, Sudan, Iraq or other countries with poor human rights records, and have come to Calais with the hope of sneaking across the English Channel to Britain, where many have relatives or the hope of obtaining work.
The statement of the former French President insisted on the active actions of the United Kingdom authorities: according to Sarkozy, Jungle migrant camp moves from Calais to the UK.
He said he wanted a new deal in which they could apply for United Kingdom asylum at a "hotspot" in France rather than having to wait to reach British soil.
Mr Sarkozy, who is attempting a political comeback at next year's election, says Britain should manage the asylum process, accepting those it wants on British territory and organising charters to remove those it rejects.
John Vine, the former independent inspector of borders and immigration, explained that France and Britain devised the treaty to deal with the previous refugee camp at Sangatte, which was hit by riots in the early 2000s.
Speaking at a rally in Le Touquet at the weekend, the former president said: "I am demanding the opening of a centre in Britain to deal with asylum seekers so that Britain can do the work that concerns them".
Currently, under Le Touquet treaty, British officials check passports in France and vice versa, but migrants in France can not claim United Kingdom asylum until they cross the channel.
In 2003, France signed a symbolic border treaty with Britain in Touquet.
"We will not continue to guard the border for Britain if it's no longer in the European Union".
As regional president, the Republican has no power to change the treaty, but he is not the first right-wing politician in France to publicly denounce it. "It would just make Calais a bigger magnet for migrants", he declared.
About 4,000 lone children are claiming asylum in the United Kingdom, with their care and resettlement down to local authorities.
"We remain committed to working together to protect our shared border in Calais and to maintain the juxtaposed controls", the Home Office said in a statement.
Sarkozy's conservative rival Alain Juppe, who opened his presidential bid on Saturday and is considered the frontrunner in the party's presidential primaries, has called on the Touquet accord to be renegotiated.
Home Secretary Amber Rudd is expected to visit Paris to discuss the treaty this week.