The pair spoke today at a joint press conference following Mr Macron’s visit to Sandhurst Military Academy.
Mrs May said that the UK and France were “Europe’s two foremost military powers” and it was “incumbent on us to demonstrate leadership in meeting the great challenges of our time and upholding the international rules-based system”.
She said the UK-France combined joint expeditionary force would be ready to deploy up to 10,000 troops “quickly and effectively to face any threat” by 2020.
The Prime Minister said: “Together we will continue to play a full role to improve the security of the continent.”And she confirmed the Bayeux Tapestry will come to the UK in 2022 after 950 years in France.
Mrs May has agreed to reinforce security at Calais with extra investment, something Mr Macron had made a top priority on his trip.
That investment is expected to come to around £44.5million.
Mr Macron said interior ministers had signed a joint treaty on the Calais border to make it smarter and more efficient with a new agreement covering unaccompanied children.
Turning to Brexit, Mr Macron said he hoped the UK’s exit would not affect its relationship with France which was rooted in “some very strong bonds”.
Emmanuel Macron and Theresa May at Sandhurst
He added: “We are facing common challenges and we are sharing the same destiny.”
Mr Macron said France’s defence and security co-operation with the UK had not been “challenged or revisited or impacted” by the vote for Brexit.
Britain’s offer of military assets in the Sahel was “a very important commitment and contribution,a strong token of your commitment and our joint willingness to work together and fight together for security”.
And he said the UK will be able to contribute to the European Intervention Initiative despite leaving the EU.
Mrs May confirmed the UK had agreed to step up support for French operations against Islamist terror groups in the Sahel region of northern France.
Emmanuel Macron met Theresa May at Sandhurst
Three UK Chinook helicopters and their crews will be deployed to the area and Britain will continue to provide heavy-lift aircraft.
France will commit troops to a UK-led battle group deterring Russian aggression in Estonia, she said.
The two leaders were briefed at Sandhurst by leaders of all the intelligence agencies from both sides of the Channel, who met for the first time ever ahead of the summit, in what Mrs May described as “underlining our unique co-operation in this field”.
Mrs May said both she and Mr Macron remained committed to the Le Touquet agreement, which allows the UK and France to post border officials on one another’s soil.
And she confirmed the UK will contribute to reinforcing security measures, including CCTV and fencing, at French ports such as Calais.
The further investment would make the UK’s borders “even more secure”, she said.
Earlier, the French president, making his first visit to Britain since entering the Elysee Palace, was greeted at Sandhurst with a guard of honour from the Coldstream Guards.
Mr Macron and Mrs May arrive at Sandhurst
Before the ceremonial welcome, the two leaders enjoyed a working lunch at the Royal Oak pub in Paley Street, in Mrs May’s Maidenhead constituency.
At the summit, Britain was expected to commit tens of millions of pounds to strengthen UK border controls in France.
Officials said the £44.5million cash injection would go towards fencing, CCTV and detection technology in Calais and other ports along the Channel.
Part of the money will also go towards helping relocate people away from Channel ports to prevent another migrant camp from forming as it did in Calais in 2015.
Britain could also commit to taking in a higher proportion of child refugees from France as part of its commitment to resettle 480 unaccompanied children under the Dubs scheme, it is understood.
The summit is also an opportunity for the two leaders to underline their countries’ enduring ties, despite Britain’s impending withdrawal from the EU.
Increasing co-operation on defence and counter-terrorism was high on the agenda at an event which saw the first meeting together of the heads of the two countries’ main intelligence agencies.
The heads of MI5, MI6, GCHQ and France’s DGSE and DGSI discussed how they can work together to counter threats such as the targeting of concert venues like Manchester Arena and the Bataclan in Paris, and terrorists using the internet as a “safe space”.
Britain was also expected to commit to participating in Mr Macron’s “European intervention initiative”, which officials do not regard as a European army but a plan to enhance co-ordination of existing armed forces.