Boris Johnson is to meet Emmanuel Macron later, hours after the French president seemed to downplay hopes of solving the Irish backstop problem.
On Wednesday, German Chancellor Angela Merkel suggested a solution to the backstop – a key Brexit sticking point – might be achievable within 30 days.
The PM said he was “more than happy” with that “blistering timetable”.
But later on Wednesday, Mr Macron insisted reopening negotiations on the issue was “not an option”.
Mr Johnson has said that the backstop – which aims to prevent a hard Irish border after Brexit – must be ditched if a no-deal exit from the EU is to be avoided.
The EU has repeatedly said the withdrawal deal negotiated by former PM Theresa May, which includes the backstop, cannot be renegotiated.
But at a news conference in Berlin with Mr Johnson on Wednesday, Mrs Merkel indicated that an alternative might be possible, stressing that the onus was on the UK to find a workable plan.
“It was said we will probably find a solution in two years,” she said. “But we could also find one in the next 30 days, why not?”
A Downing Street spokesman described the meeting of the two leaders as “constructive”.
However, hours later, Mr Macron appeared to downplay the prospects of a breakthrough, telling reporters in Paris: “Renegotiation of the terms currently proposed by the British is not an option that exists, and that has always been made clear by [EU] President Tusk.”
BBC political correspondent Ben Wright said Mr Johnson was likely to get a “chillier reception” from Mr Macron, who sees Brexit as “contaminating the whole European project” and wants it over and done with.
For weeks, EU leaders have said Boris Johnson’s demand for the Brexit deal to be reopened is a non-starter and not up for discussion.
But after dinner with Chancellor Merkel, a Downing Street source said there was a glimmer of light where there wasn’t a day before.
But for three years the EU has been unpersuaded that any technical solutions currently available would eliminate the need for a backstop to be in the withdrawal agreement.
Boris Johnson wants the UK out of the single market and the customs union, so there will be different tariff and regulatory systems on each side of the border.
And – while Chancellor Merkel sounded conciliatory – Mr Johnson could find a chillier reception in Paris.
President Macron is clearly losing patience with the Brexit crisis and has bluntly said the deal is closed.
The French president also said a trade deal with the US would not make up for the “cost” of what he called a “hard Brexit”.
President Trump’s national security adviser, John Bolton, has previously said the US supported a no-deal Brexit, adding that Washington would propose an accelerated series of trade deals with the UK.
But Mr Macron said: “Can the cost for Britain of a hard Brexit – because Britain will be the main victim – be offset by the United States of America? No.
“And even if it were a strategic choice it would be at the cost of a historic vassalisation of Britain.
“I don’t think this is what Boris Johnson wants. I don’t think it is what the British people want.”
Mr Macron added that “the British are attached to being a great power” but after Brexit could become merely a “junior partner” of the US.
Earlier on Wednesday, an official in Mr Macron’s office said France now saw a no-deal Brexit as the most likely scenario.
The UK is due to leave the EU on 31 October, with no deal being the default option.
Mr Macron said he saw no reason to grant a further delay to Brexit unless there was a significant political change in the UK, such as an election or a new referendum.
French officials said if the UK requested an extension in order to hold a new election, the EU would probably grant it.
After meeting Mr Macron on Thursday, Mr Johnson will attend the G7 summit on Saturday alongside other leaders including US President Donald Trump.
Meanwhile, Labour Party leader Jeremy Corbyn has cancelled a trip to Ghana later this week, urging opposition MPs to meet urgently to discuss ways to prevent a no-deal Brexit.
Mr Corbyn has proposed that in order to prevent a no-deal exit, opposition MPs should help him defeat the government in a no-confidence motion and install him as a caretaker PM.
If he wins the vote, he plans to delay Brexit, call a snap election and campaign for another referendum.
However the Liberal Democrats, and some potential Tory allies opposed to a no-deal exit, have indicated they will not back a plan that leads to Mr Corbyn in No 10.