The two leaders arrived at the Sandhurst military academy near London for the wide-ranging talks, following lunch at the Royal Oak pub in May's Maidenhead constituency.
The French flag was flying at the academy where the two were greeted by a guard honour and the sounds of the French national anthem on a rainy day.
Macron's arrival comes hours after the UK government pledged an extra 44.5 million (50 million euros, $62 million) to boost security around Calais following a request from Macron.
While the two countries cooperate closely in numerous areas, including intelligence and defence, differences over migration have strained ties.
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The money would be on top of more than 100 million already paid by Britain following a border deal between the two countries that has now been renegotiated and is due to be signed on Thursday.
The announcement followed France playing its own diplomatic card with a promise to loan Britain the Bayeux Tapestry.
May's Downing Street office said the summit was an opportunity to "further our shared aims and ambitions and demonstrate our close ties."
The British and French leaders also aim to deepen cooperation in tackling terrorism at the meeting, as the UK tries to strengthen bilateral ties before leaving the European Union in March 2019.
The gathering at Sandhurst military academy -- the 35th UK-France summit -- is expected to focus on the sensitive issue of immigration as hundreds of people continue to camp out in Calais.
The two countries currently abide by the 15-year-old Treaty of Le Touquet, which permits immigration checks within each other's borders.
A new treaty will be signed at Thursday's summit to complement the 2003 deal, according to French officials.
The extra 44.5 million pledge was criticised in the British press, with the right-wing Daily Mail calling the Bayeux Tapestry offer as "a sweetener" and dubbing the Calais agreement "Le Stich-up!"
Macron is expected to confirm on Thursday that France will agree in principle to loan the fragile 941-year-old embroidery.
Despite Brexit dominating the political debate in the UK, the issue is not scheduled for formal discussion at the summit but it will likely come up in talks on other topics, a British official said.
The British prime minister is also set to commit to sending Royal Air Force (RAF) helicopters to a key French counter-terrorism operation in Mali.
The deployment of three RAF Chinook helicopters to provide logistic support to French troops tackling jihadis across Africa's Sahel region is part of broader counter- terrorism and military efforts there by the UN, the EU and the African Union.
"Recent terrorist attacks across Europe underline the scale of the cross-border challenge we face in keeping our citizens safe," a UK government spokesman said.
France in turn has agreed to commit troops to the British-led NATO battlegroup in Estonia in 2019.
At the summit the pair will also discuss their joint crackdown on online extremism "to ensure that the internet cannot be used as a safe space for terrorists and criminals," the spokesman said.
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