Britain will agree to take in more young refugees while providing "significant" funds for northern France's economic development under a new border agreement to be struck between Emmanuel Macron and Theresa May on Thursday, French sources have told AFP.
His strong words come as France bids to encourage London-based banks to relocate to Paris.
He said it was up to the UK Government to work out if it wanted a Norway-style deal - where the country is signed up to the single market - or a free trade agreement similar to that signed by Canada.
The money will be on top of more than £100 million already paid by Britain, following a request by Macron to contribute more cash.
"I am here neither to punish nor to reward", said Macron.
Brexit was not formally on the agenda at the summit, where ministers including foreign secretary Boris Johnson and culture secretary Matt Hancock met their French counterparts to signal the breadth of cooperation between the two countries on issues from artificial intelligence to weapons construction.
Peter Allen said French President Emmanuel Macron is very good at packaging up a poor deal in very friendly terms - and the Prime Minister has fallen for it.
"And as our efforts in the Sahel and across Africa demonstrate, we will work together to address the instability which fuels it. President Macron and I have both confirmed that the United Kingdom and France remain committed to the principles of the longstanding Le Touquet agreement, under which the U.K.is able to carry out full border checks on French soil". European Union officials warn the U.K.it can't hang on to the benefits of membership without accepting its responsibilities, including free movement of people.
Speaking at the UK-France Summit, May said Brexit would not impact the relationship between Britain and France, or indeed the rest of Europe.
The U.K. also said it will send three Royal Air Force Chinook helicopters and dozens of personnel to join France's military mission against Islamic militants in Africa's Sahel region.
"What a stitch-up! Did borrowing the Bayeux Tapestry cost Britain 45 million pounds more to stop migrants at Calais?" the Daily Mail asked, while the Sun mocked up the depiction of how William the Conqueror invaded England in 1066 as a tale of the European Union trying to stop Britain leaving the bloc.
The massively overcrowded centre, set up in 1999, was shut in 2002 under pressure from London, which saw it as a magnet for migrants trying to cross the Channel to reach Britain.
There were choreographed displays of cordiality, including a loan to Britain of the 11th-century Bayeux Tapestry and a lunch visit to a Michelin-starred pub in May's own constituency in the southern English town of Maidenhead.