Theresa May is cutting short her summer break in Italy to meet the French president, Emmanuel Macron, to try to persuade him to soften his approach to Brexit.

The prime minister will become the first foreign leader to meet Macron at his summer home, Fort de Brégançon, in the south of France on Friday in an attempt to convince him to sign him up to her Chequers deal.

The French government has not entirely rejected the UK’s latest Brexit plan, although Macron is thought to be foremost among European leaders to have privately expressed concerns about whether it could work.

The meeting, which will conclude with a private dinner also attended by the leaders’ spouses, Philip May and Brigitte Macron, is part of the government’s strategy to go over the head of the European commission and engage with national leaders directly.

The foreign secretary, Jeremy Hunt, on Tuesday appealed directly to France and Germany to try to force the commission to strike a “sensible and pragmatic” Brexit deal.

However, French officials have warned that Macron would be unlikely to accept any deal that bypassed Brussels, even as May is trying to address key issues over security cooperation and financial services.

May is meeting other European leaders in Salzburg at the end of September to try to reach some sort of compromise on Brexit.

Ahead of talks with his opposite number in Paris, Hunt accused Brussels of waiting for Britain “to blink” in negotiations as he claimed the chances of the UK leaving the EU without a deal were “increasing by the day”.

“That is just a profound misunderstanding of us as a nation,” he said.

“There is real chance of no deal by accident. Everyone is assuming, no, no, no, this will never happen. Well, actually, it could.”

In an interview before his trip to France, Hunt told the EU’s chief negotiator, Michel Barnier, that his approach to the talks would inflict a “breakdown in relations and trust” between Britain and the continent, which would be a “profound geostrategic mistake”.

“The probability of no deal is increasing by the day until we see a change of approach from the European commission, who have this view that they just need to wait and Britain will blink,” he told the Evening Standard.

“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.”

However, Brussels insiders have repeatedly said Barnier and his negotiating team are only acting on the orders of France, Germany and the rest of the 27 EU countries. Any inflexibility originates from the nation states.

Hunt warned that a no-deal Brexit would be an economic “tragedy” for Britain and Europe. “If it became harder for European businesses to access finance, that is far from trivial,” he said, alluding to the flow of money from the City of London.