In a memorandum leaked to the Mail On Sunday, he said his talks in Paris have been “the worst I have had anywhere in the EU”, with the French open about their desire to see the UK weakened.
Following a visit to the French capital earlier this month, Mr Browne said the mood had been made “more giddy and more assertive” by the election of President Emmanuel Macron.
His comments will reinforce fears among critics of Brexit that other EU countries will exploit the UK's withdrawal to take away lucrative business.
Mr Browne, who met banking chiefs, senior politicians and diplomats, wrote: “They are crystal clear about their underlying objective: the weakening of Britain, the ongoing degradation of the City of London.
“The meeting with the French Central Bank was the worst I have had anywhere in the EU. They are in favour of the hardest Brexit. They want disruption. They actively seek disaggregation of financial services provision.
“Every country, not unreasonably, is alive to the opportunities that Brexit provides, but the French go further, making a virtue of rejecting a partnership model with Britain and seemingly happy to see outcomes detrimental to the City of London even if Paris is not the beneficiary.”
Mr Browne, who was a Liberal Democrat minister in the coalition under David Cameron and Nick Clegg, said hostility to the UK is not confined to a few officials but represents a “whole-of -France collective endeavour”.
“The clear messages emanating from Paris are not just the musings of a rogue senior official in the French government or central bank. France could not be clearer about their intentions. They see Britain and the City of London as adversaries, not partners,” he wrote.
“What we are witnessing is a whole-of-France collective endeavour, made both more giddy and more assertive by the election of Macron.
“It is entirely in line with the tone set by French representatives currently crashing conspicuously around London, making heroic relocation promises and pouring cold water on the propositions of alternative EU financial centres.”
He said the French assertiveness is even beginning to alarm other EU member states who fear they could find themselves isolated if they seek to maintain good relations with the City and the UK.
“There is plenty of anxiety elsewhere in the EU about the French throwing their weight around so aggressively, but their destructive impulses are not being confined, and other EU countries that want a friendly relationship with Britain and the City of London are being marginalised,” he wrote.
Meanwhile, former cabinet secretary Lord O'Donnell said ministers need to end their squabbling over Brexit and come to an agreed position if they want a successful negotiation.
Writing in The Observer, he said: “The EU has clear negotiating guidelines, while it appears that Cabinet members haven't yet finished negotiating with each other, never mind the EU.”
He said the Government should be “honest” about the scale of the challenge and the need for an extended period of transitional arrangements after the UK leaves in 2019 while a final settlement is agreed.
“There is no chance all the details will be hammered out in 20 months,” he said.
“We will need a long transition phase and the time needed does not diminish by pretending that this phase is just about 'implementing' agreed policies as they will not all be agreed.”
Sir Nigel Sheinwald, a former ambassador to the EU, said there is a “one-in-three” chance of the talks collapsing unless the UK adopts a more realistic approach, including over Britain's so-called “divorce bill”.
“I think [the negotiations] could break down quite quickly if, after the autumn, our position on these fundamental issues - the financial settlement, and then the fundamentals of our future relationship - don't move more in the direction of common sense and economic sense,” he told The Observer.
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