The application still pending are for access to the sensitive 6-12 nautical mile zone.
France warned on Thursday that if the 53 licences still awaiting UK approval are not granted by Friday evening, it would call on the EU to go "to litigation".
Annick Girardin, France's sea minister, made the announcement during a hearing with a senatorial committee.
"If all the licences are not granted by tomorrow evening (the deadline set by Brussels for London to settle fishing disputes), France will request a meeting of the partnership council", which is supposed to guarantee the application of the post-Brexit agreement, "to note the failure of the United Kingdom to respect its signature," Girardin said,
"It is the Commission that will take the litigation and retaliatory measures if they must be applied," she added.
But Downing Street said London did not accept the Friday deadline.
"We've never set a deadline. I recognise they (the EU) themselves have set one but it's not one we're working to," Prime Minister Boris Johnson's spokesman told reporters.
The UK has issued 1,004 licences to French fishing boats but 94 licences are still pending, Girardin said.
Under the Brexit trade deal concluded just before Christmas 2020, EU fishing boats can continue to fish in British waters if they obtain a licence.
But they need to prove that they previously were fishing there — a requirement that smaller French boats, lacking the appropriate technology, have found difficult to fulfil. Many have failed to secure licences from authorities in the UK or the Channel island of Jersey.
France argues the boats are well known to the British authorities and their past records are common knowledge, although some French commentators question their strict rights under the letter of the law.
The British government has said it has issued licences for 98% of the French applications it received and to all those who demanded access to the 12 to 200 nautical mile zone away from the coast.
In the sensitive 6-12 nautical mile zone, however, 31 of 50 licences for vessels under 12 metres were still pending in early November as were three of 88 applications by vessels over 12 metres.
The Island of Jersey has meanwhile approved 113 of 217 applications with a further 49 temporary licences granted until the end of January 2022 to allow these vessels more time to supply the necessary evidence.
Girardin said that overall 53 licences for access to the 6-12 nautical mile zone are still pending, "40 of which are requested for replacement vessels (new boats bought by fishermen to renew their fleet)" and which she said London refuses for the moment to consider.