The existing 2003 Le Touquet border agreement was widely criticised in France after the town of Calais became a hub for refugees hoping to travel to Britain.
Other commitments include the deployment of three RAF Chinook helicopters in Mali, where French forces are fighting Islamist militants, and France sending more troops to reinforce a British contingent in Estonia on Nato's border with Russian Federation.
"I want to make sure the Single Market is preserved because that's at the heart of the European Union", the president said.
French President Emmanuel Macron said on Friday that the Islamic State group in Syria and Iraq would be defeated militarily "in the coming weeks", as he laid out plans for bolstering France's defence capabilities.
May said she believed it is in the interest of both Britain and the European Union to continue to have a good economic partnership with Britain.
The French government recorded 115,000 attempts to enter the United Kingdom from Calais in 2017 compared to 165,000 the previous year.
But asked about the EU's refusal to negotiate trade access for British financial services outside the single market, Mr Macron said: "The choice is on the British side, not on my side".
Bitcoin slides to below $10000
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Downing Street said in a statement later that the two countries are the only European powers with the ability and political will to deploy and sustain significant military force.
The French President did the honour of taking the photo but it was uploaded to Mrs May's Twitter profile this morning.
Furthermore, the two countries will seek to reduce the number of people attempting to cross the border illegally "at risk to safety and life" and to "reduce migratory pressure at the shared border and on the French side of the Channel and North Sea".
"There must be no hypocrisy in this respect, otherwise it will not work or we would destroy the single market and its coherence", said Macron.
In November, Collomb said there were about 300,000 undocumented migrants in France, and the government registered a record 100,000 asylum claims a year ago.
The Prime Minister also spelled out her wish for a "good ongoing security relationship with the EU" after Brexit, with all the intelligence chiefs of both France and Britain having met for the first time in history earlier on Thursday.
A French human rights commission in 2015 said the accord had made France the "police branch" of Britain's immigration policies.
But the two leaders were forced to inspect the troops in the freezing rain at the start of the summit, at the Berkshire military academy, when the skies opened for the guard of honour.