Alain Juppé, a center-right former prime minister who is considered a frontrunner in next year's elections, told journalists that he is seeking a renegotiation of the 2003 Le Touquet accord, which, because it allows England to check passports in France, in effect situates the border to Britain on French territory.
The policy has resulted in thousands of migrants converging on the controversial "Jungle" migrant camp outside the French port of Calais, as they attempt to smuggle themselves across the Channel.
"We can't tolerate what is going on in Calais, the image is disastrous for our country and there are also extremely serious economic and security consequences for the people of Calais," Juppé said, in a Paris interview with The Guardian and a number of European newspapers.
"The first thing is to denounce the Le Touquet accords. We cannot accept making the selection on French territory of people that Britain does or doesn't want. It's up to Britain to do that job," he said.
Britain: 'Nothing has changed'
Under the terms of the existing accords, immigration officials from both countries are able to check passports on each other's soil.
As a consequence, slum-like camps have become permanent fixtures on the French landscape, namely at the "Jungle" outside Calais, which is near a 50-kilometer (31 miles) undersea tunnel to the UK, and elsewhere along France's northern coast.
A Downing Street spokesman responded to Juppé's remarks by insisting the deal would not change: "The French and UK governments have been absolutely clear in their commitment to the Le Touquet agreement. Nothing has changed."
The spokesman said that Britain's Home Secretary Amber Rudd had had two meetings with her French counterpart at which the issue had been discussed, "and it's been made perfectly clear that both the French government and the British Government are committed to the Le Touquet agreement."
"Nothing has changed and there is no plan at all for it to be torn up," he added.
Asked whether British Prime Minister Theresa May was concerned that the position might change after the presidential elections in May, the spokesman said: "That's something that will happen in the future. The current French government is clearly of the same view as the British Government that the Le Touquet agreement is working."
Politicians in both countries, including then British Prime Minister David Cameron and then French Economy Minister Emmanuel Macron, warned that the border could shift to the UK
if British voters chose to leave the European Union in a June referendum.
Voters narrowly voted to quit the EU, and the terms of Britain's future relationship with Europe are yet to be negotiated.
"The Jungle," a makeshift, unregulated settlement that is not recognized by French authorities, has been an unwelcome presence in Calais, sparking regular protests from locals calling for its closure.
After much agitation, it is due to be demolished by authorities later this month, with the residents to be either relocated or deported.
Although numbers at the camp are constantly in flux, thousands live there. French officials said this week that there were more than 6,000 people living in the camp, while aid organizations put the number at 10,000.
The vast majority are young men, predominantly from countries such as Afghanistan, Eritrea, Sudan, Iraq, Pakistan, and Syria, although there are also hundreds of women and children.
Earlier this week, a group of unaccompanied teenage refugees from the camp arrived in Britain
, where they had been accepted for resettlement under European Union common asylum rules.
Generally, the migrants hope to enter Britain illegally by smuggling themselves on trucks or other vehicles. Despite the wretched conditions in the dangerous and unhygienic camp, many are reluctant to leave and register in a French reception center, as that would prevent them from reaching their preferred destination, the UK.