David Cameron is to visit Paris on Monday evening for talks with President Francois Hollande ahead of a crunch EU summit on Thursday.
Securing French agreement to a package of EU reforms will be crucial if a deal is to be reached in Brussels at the end of this week, clearing the way for a referendum on UK membership before the summer.
Mr Cameron is insisting on legally-binding assurances that countries which do not use the single currency will not face discrimination as the eurozone integrates further.
But France has made clear that it will resist anything which looks like special treatment for the City of London.
The visit to Paris comes a day before Mr Cameron speaks to leading MEPs in Brussels on Tuesday, and follows his trip to Hamburg on Friday for talks with German Chancellor Angela Merkel – as his round of whirlwind diplomacy gathers pace in the run-up to the two-day European Council summit.
Mr Cameron’s trip comes as the chairman of HSBC Group voiced the bank’s support for the UK to remain in a reformed EU.
HSBC has announced that it will keep its headquarters in the UK after a high-profile lengthy review.
But group chairman Douglas Flint said that work and staff could be transferred from London to Paris if the referendum, due before the end of 2017, results in UK withdrawal from the EU – or Brexit.
Mr Flint told the BBC Radio 4 Today programme: “We did a major piece of economic research a year ago which said, in our view, Britain had benefited from Europe and that the best answer economically was for Britain to be within a reformed Europe pushing for completion of the single market, particularly in services.
“Now we are lucky in the sense that we have a major bank in France. So, if we were to leave and if there were to be restrictions, ultimately on the renegotiation of Britain’s position, we have the ability to move activity and people between London and Paris.
“But our strong economic view is that Britain is better within a reformed Europe.”
But the chief executive of the Vote Leave campaign for EU withdrawal, Matthew Elliott, said HSBC’s decision to retain its HQ in London showed the In campaign’s warnings that Brexit would drive business out of the UK were “baseless scare stories”.
“When we vote Leave we will be able to negotiate a new friendly deal with the EU that will allow financial firms in the UK to continue to trade across Europe and the globe,” he said.
“The UK is a great place to invest and do business and will become even more attractive after we vote Leave.”
Securing a deal this week on the package of EU reforms drawn up by European Council president Donald Tusk is all-but-essential if Mr Cameron is to press ahead with a referendum on June 23, which is widely thought to be his preferred date.
As well as French concerns over financial proposals, he is also facing objections from eastern Europe to plans to scale back welfare payments to migrant workers, with countries such as Poland thought to be holding out for any restrictions to be applicable to the UK only.
Foreign Secretary Philip Hammond – who was attending an EU foreign ministers meeting in Brussels on Monday – predicted discussions over the membership terms would run “right to the wire” of the summit of the 28 national leaders.
But just as vital is convincing senior Government figures to support the deal, amid reports that Attorney General Jeremy Wright is considering backing Leave in the looming referendum campaign.
Justice Secretary Michael Gove is thought to be among a handful of Cabinet ministers wavering, while London mayor Boris Johnson has declared he will make his views known with “deafening eclat” when an agreement is sealed.
Mr Cameron is also coming under pressure to free Eurosceptic ministers from collective responsibility quickly after striking a deal.
Graham Brady, chairman of the influential Tory backbench 1922 Committee, insisted the Cabinet should be gathered on Saturday or even Friday night after the conclusion of the summit.
I think that is absolutely essential, he told Sky News. “It is in everybody’s interests to do this as quickly as possible and if it were to appear that David Cameron was seeking to have the whole weekend to himself to put one side of the argument, I think that would look bad for the Remain campaign.