Disagreements on key issues, such as fisheries, have hampered progress in recent months.
Michel Barnier, the EU’s chief negotiator, warned ambassadors last week that they had to be “realistic” about the chances of ensuring full access to British waters for European trawlers.
France is one of eight coastal states that have long insisted that fishing rights should remain unchanged.
They argued that this is the price Britain must pay if it wants a zero-tariff, quota-free free trade agreement with the EU.
But in an interview with France Info radio on Sunday, French Minister of European Affairs Clément Beaune alluded to a possible compromise.
“If we told our fishermen that we have drastically reduced their access to UK waters – on which they depend for their economic survival – they would say it is indecent and they would be right. ”
“However, after Brexit, it won’t be the same as before.
“But we will stand up tooth and nail on the best interests of our fishermen, our farmers, our businesses and our citizens in general and we will not accept a bad deal. ”
Read more: The British fishing industry or Brexit’s red herring
David Frost, Britain’s chief negotiator, says the UK wants to conduct annual negotiations with the bloc on fishing quotas in the same way Norway does.
“The United Kingdom sees it as a lever to access the European Union market, it is the game,” said an EU ambassador, speaking on condition of anonymity.
The two sides also disagree on how to control any future trade deal.
The UK also rejects the EU’s position that it must closely follow its state aid rules, which are defined as financial aid or tax breaks that governments give to businesses.
EU governments fear Britain is trying to gain an unfair advantage by seeking to enforce different regulations.
Leaders will meet in Brussels on Thursday to assess whether a deal is within reach.
EU diplomats say they will decide whether to continue negotiations or prepare for a no-deal Brexit.
The UK is now in a transition period with the EU until December 31, 2020, which means it still follows EU rules and trade remains the same.
If no deal is reached, the UK and the EU would have to fall back on World Trade Organization (WTO) rules, which would result in a series of tariffs on goods.
jf / aw