The UK and France are "making a new tapestry together", Emmanuel Macron said as he agreed new co-operation on defence and measures to tackle the migrant crisis with Theresa May.
The talks saw Mrs May commit tens of millions of pounds to strengthen UK border controls in France while Mr Macron confirmed the loan of the Bayeux Tapestry to Britain.
But Mr Macron indicated he would stand firm on the issue of financial services during the Brexit talks, saying he was "here neither to punish nor reward" the UK following its decision to leave the European Union.
A new treaty between the two countries will enable the improvement of security at Calais, costing the UK around £45 million.
The treaty will also allow an acceleration in the processing of migrants seeking to come to the UK via Calais, with a reduction from six months to one month for adults and 25 days for children.
Mr Macron said that the current situation in Calais was "not satisfactory".
But he said the new treaty would allow him to fulfil his 2016 vow that after Brexit "migrants will no longer be in Calais".
He said: "We can either manage the border together or it will be a disastrous situation. It is not a gift for France. It is some joint management. "
The French president, making his first visit to Britain since entering the Elysee Palace, was greeted at the Royal Military Academy, Sandhurst, with a guard of honour from the Coldstream Guards.
The choice of venue was appropriate as the countries committed to closer defence and security co-operation between "Europe's two foremost military powers", Mrs May said.
But Brexit loomed over the summit, with Mr Macron saying he regretted the British decision to leave, even if he respected the will of the British people.
Asked why he wanted to exclude financial services from a future UK-EU free trade agreement, Mr Macron said: "I am here neither to punish nor to reward.
"I want to make sure that the single market is preserved because that is very much the heart of the EU.
"The choice is on the British side, not on my side. But there can be no differentiated access for the financial services.
"If you want access to the single market - including the financial services - be my guest. But it means that you need to contribute to the budget and acknowledge European jurisdiction.
"Such are the rules, and we know the system already in place for Norway."
Mrs May restated her call for a deep and special partnership and comprehensive trade agreement between the UK and EU after Brexit.
"We recognise that as we leave the EU we will no longer be full members of the single market," she said.
But it was in the interests of both sides in the talks to have a trade deal that covered both goods and services, she said.
"I think the City of London will continue to be a major global financial centre.
"That is an advantage not just for the UK, it's actually good for Europe and good for the global financial system."