The Prime Minister will join the French leader at his holiday home near Toulon on Friday as the rhetoric around a no deal outcome ramps up.
Her visit comes amid reports that ministers are to try to bypass Brussels to appeal to European heads of government directly on their proposals.
A Downing Street source told the Telegraph: “We need to crack on [in the talks]. France and Germany have always been important in the Brexit negotiations.”
It comes just a day after Jeremy Hunt called on Mr Macron and German Chancellor Angela Merkel to urge the EU to relax its tough negotiating stance, as the prospect of Britain crashing out without a deal grew “by the day”.
The new Foreign Secretary said the approach taken by the European Commission’s chief negotiator Michel Barnier could inflict a “breakdown in relations and trust between Britain and European countries”.
Ahead of talks with French foreign minister Jean-Yves Le Drian in Paris yesterday, he told the Evening Standard: “There is a real chance of No Deal by accident. Everyone is assuming, no, no, no, this will never happen. Well, actually, it could.
“France and Germany have to send a strong signal to the Commission that we need to negotiate a pragmatic and sensible outcome that protects jobs on both sides of the Channel because for every job lost in the UK, there will be jobs lost in Europe as well if Brexit goes wrong.”
Last week, Nathalie Loiseau, the French minister for European affairs, said “we would all suffer” if Britain was unable to reach an agreement with Brussels but that it would be “worst” for the UK.
The latest round of talks also comes amid warnings that four lanes of the M20 could be used as a 13-mile long lorry park for up to four years after Brexit.
A set of impact reports – obtained by Sky News – show that Conservative-run Dover District and Kent County councils have a string of concerns about the Government’s plans for handling disruption at the border when the UK leaves the European Union.
The latter warns that the Government’s permanent fix of setting up new lorry parks “will not be delivered until 2023 at the earliest”.
Last week Downing Street confirmed Mrs May would be going to Italy and then Switzerland on holiday, with a gap in between to return to the UK and to attend a First World War memorial event in Amiens.