"Our shared history is reflected in the loan of the Bayeux Tapestry to the United Kingdom in 2022, the first time it will be on British soil in more than 900 years", May said in a statement as she welcomed French President Emmanuel Macron on a visit to Britain.
"If you want access to the single market - including the financial services - be my guest", he said.
Speaking to Marr, he warned that the United Kingdom could not "cherry-pick" the elements it wanted.
The BBC reported Macron saying the United Kingdom could have "deeper relations" with the European Union than other countries, but maintained stopping short of full Single Market access since Britain is leaving the bloc.
He stressed that the United Kingdom would not be able to gain access to the single market without first agreeing to "preconditions", which would include freedom of movement, budget contributions and the jurisdiction of the European court of justice.
The announcement came as U.K. Prime Minister Theresa May and French President Emmanuel Macron held a bilateral summit Thursday meant to strengthen security and intelligence ties between the neighboring nations, and to build goodwill as Britain negotiates its exit from the European Union.
In a speech, Mrs May reiterated that her government are approaching negotiations "looking for a deep and special partnership, comprehensive trade agreement, and also a strong security partnership".
But the cold water on that argument is that every EU member benefits from the European single market.
"We're leaving the European Union, but not Europe", she told Germany's Bild tabloid.
'It doesn't make sense, ' he told Marr.
Theresa May and the French President, Emmanuel Macron, have committed to speeding up the process by which refugees in France are able join family in safety here in Britain.
"I do respect this vote, I do regret this vote, and I would love to welcome you again", he said.
"When I look at your debate it was too much favourable just for the City and less favourable for the rest of the country", he said. "I think it's important that politicians then deliver on that".
"It is vital that any measures taken by Governments to protect their borders, including those that form a part of this Treaty, do not prevent refugees being able to seek protection or reach loved ones in the United Kingdom through safe routes". The UK also announced an extra £44.5m to be spent on beefing up Channel border security.
Media captionBridge designer Ian Firth and engineering expert Dave Parker on whether a bridge is feasible.
In an interview recorded for BBC One's Andrew Marr Show tomorrow, Mr Macron said there is "a competition between different countries" to attract financial services companies in the future and that France wanted "to attract the maximum activity".