European Union officials warn the United Kingdom it can't hang on to the benefits of membership without accepting its responsibilities, including free movement of people. He also said Britain could not have the same level of access to areas such as financial services once it left the EU.
"I think the City of London will continue to be a major global financial centre".
During the contentious French presidential campaign of 2017, Macron vowed to renegotiate the agreement.
But in a country whose future relationship with Europe remains uncertain, others said the meeting - with its broad agenda on intelligence, security and migration - was a sign that despite Brexit, cooperation between France and Britain can survive.
Mrs May treated the French leader to a pub lunch of crab and duck breast, followed by a serving of British military pomp.
Earlier the two leaders met the Coldstream Guards during a downpour at Sandhurst and watched a flypast by an RAF Typhoon and French air force Dassault Rafale.
Amid a sudden hailstorm, Mr Macron and Mrs May inspected the honour guard before taking a salute from soldiers on horseback.
Migrants at Calais will be fast-tracked into Britain under new plans agreed by Theresa May as she bowed to further pressure from the French. French President Emmanuel Macron demanded the extra funding to help with the hundreds of migrants at the Port of Calais. In addition to paying more for work on the ground, for instance, Britain will slash the processing time for unaccompanied migrant children seeking asylum from six months to 25 days.
The original Le Touquet text, which came into force in February 2004, implemented joint controls at coastal ports in both countries as Britain, which is not part of Europe's Schengen visa-free zone, looked to bolster efforts to keep migrants out.
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He missed out on his hundred, though, after being caught sensationally by Niroshan Dickwella off Nuwan Pradeep in the 19th over. The previous fastest T20I century among India batsmen was 46 balls by KL Rahul, against West Indies in Lauderhill past year .
Instead she stressed the need to clamp down on people smugglers and take other measures to stop migrants from getting to Calais.
Mr Macron said the current situation in Calais was "not satisfactory".
Britain was expected to pledge to send three Chinook helicopters to Mali to provide logistical support for a French counter-terrorism operation and to participate in a new European defence initiative, the European Intervention Initiative. France has led efforts to fight al-Qaida and IS-linked jihadi groups in the vast region south of the Sahara desert. France and Britain have both faced a string of violent attacks by extremists inspired or directed by the Islamic State group.
"The President and I agree on the importance of the UK-France relationship, not just to our security but to European security..."
In return, France will send troops to join a UK-led North Atlantic Treaty Organisation battle group in Estonia in 2019, aimed at countering an increasingly assertive Russian Federation.
Migrants hoping to stow away on trucks bound for Britain have always been drawn to France's northern coast, with the squalid "Jungle" camp near Calais once housing some 10,000 people before it was bulldozed by the government in late 2016. It will go on display at an unspecified British venue in 2022.
-French summit "will underline that we remain committed to defending our people and upholding our values as liberal democracies in the face of any threat, whether at home or overseas".
He said: 'We can either manage the border together or it will be a disastrous situation.