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Theresa May is in talks with Emmanuel Macron as she steps up her efforts to win backing for her Brexit plans.
The UK prime minister has cut short her holiday for talks at the French president's summer retreat.
It comes after UK Brexit Secretary Dominic Raab held talks with his counterparts in Paris on Thursday.
The UK's former ambassador to France has warned Mrs May not to expect a Brexit breakthrough in her talks with the French president.
Lord Ricketts told the BBC that Mr Macron was "the last person" to want to break ranks with the rest of the EU to push for a softer stance from Brussels.
Mr Macron "doesn't believe in softening" the position on Brexit as "he is a passionate pro-European", the peer said.
Mrs May spoke by phone to European Commission President Jean-Claude Juncker about Brexit and global trade on Friday morning, ahead of her meeting with Mr Macron.
Mrs May's visit has been described in the French press as a "cry for help".
The meeting with President Macron at his summer retreatreportedly at her requestis seen as a bid to circumvent the European Commission and, according to the editorials here, exposes "obvious" British anxiety.
The centre-right Le Figaro has a particularly colourful editorial which pictures Mrs May trying to wrest the steering wheel of the Brexit car from different factions of her party back home, as it "jolts over the London potholes and skids on the oil slicks of Brussels".
Never mind "take back control" the paper says, Britain has lost control of Brexit.
After Michel Barnier's chilly response to Mrs May's Brexit plan last month, this visitwhich cuts short her summer walking holidayis part of a charm offensive by the British government to see what progress can be made with individual European leaders.
Many here in France believe the chance of a "no deal" Brexit is growing.
But that pressure is unlikely to deliver the kind of concessions the prime minister would like.
Mr Macron is a pragmatic man, but he has staked his presidency on a strong EU, and has so far stuck fast to core principles on the single market.
France may show a little flexibility later in the game, one former French official told me, but not the kind of flexibility on which Britain is currently banking.
The two leaders are meeting at Mr Macron's summer residence in Fort de Brégançon, on a small island off the French Mediterranean coast.
After the hastily-arranged talks, Mrs May and her husband Philip will join the president and his wife Brigitte for a private dinner.
The prime minister is ending her break in the Italian Lakes a day early for the talks, although she will fly to Switzerland for a second break later this month.
On Thursday, EU chief negotiator Michel Barnier signalled a willingness to be flexible in Brexit negotiations around the Northern Ireland border.
Calling the issue "the biggest risk" caused by Brexit, Mr Barnier said he was "ready to improve" the EU's proposals.
The EU wants Northern Ireland to be part of a common regulatory area for goods and customs if a trade deal has not been reached by the end of the planned 21 month post-Brexit transition periodsomething the UK has rejected.
Mr Barnier was also positive about reaching a free trade deal "unprecedented in scope and depth".
He warned that any deal must not undermine free movement of goods, capital, services and labour within the EU single market by setting up free movement in goods only.
But he also said: "I remain confident that the negotiations can reach a good outcome.
"It is possible to respect EU principles and create a new and ambitious partnership."