During last year's French election campaign, Mr Macron said he wanted to renegotiate or scrap the 2003 Le Touquet agreement, which established French border controls in Britain and United Kingdom controls in Calais.
The tough message risked putting a sour note at the end of a meeting created to show the strength of Anglo-French relations, despite the UK's exit from the EU.
France also wants Britain to take in more migrants from Calais, especially unaccompanied children. France will lend Britain the Bayeux Tapestry, an 11th century treasure that tells the tale of how William the Conqueror came to invade England in 1066, an official at the presidential Elysee Palace in Paris said yesterday.
"The choice is on the British side, not on my side", Macron said at the joint press conference. "You want to accept a single market with finance being part of it?"
May said Britain would not be a full member of the European Union single market after leaving the bloc, but was seeking a "comprehensive" free trade deal.
Mr Macron initially hailed the coalition agreement as "good news" for France and for Europe, but he has not wholeheartedly embraced Mrs Merkel's new pro-European programme of government, crucially disagreeing on the question of the European Monetary Fund, which he does not believe is needed.
She stressed that the deal with the French would "enhance the security of our border" and would in turn reduce the number of migrants coming to the UK.
It was all smiles when President Macron and Theresa May posed for a selfie at the French-British summit's official dinner at last night at the V&A Museum.
"They can have no differentiated access to the financial services".
The summit between Mrs May and Mr Macron, at the Royal Military Academy Sandhurst in Berkshire, also featured the first meeting of the heads of Britain and France's five intelligence agencies, and is being attended by British cabinet ministers and their French counterparts.
During his election campaign, Macron said that he wanted to scrap the 2003 Le Touquet agreement which first implemented the French border controls in Calais.
Commitments will be made to a 10,000-strong Franco-Anglo combined joint expeditionary force to be ready by 2020.
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.
In turn, France is offering more troops to reinforce a British contingent deployed in Estonia under NATO's mission to deter Russian aggression.
Instead she stressed the need to clamp down on people smugglers and take other measures to stop migrants from getting to Calais.
Macron is also expected to announce the possible loan of the 950-year-old Bayeux Tapestry to Britain under a programme of exchanges of artworks between the two nations.