One boat skipper said the island’s government should shut large areas off the coast to all fishing boats – including Jersey’s – if the situation does not improve.
Despite the reprieve, the island’s fishermen have been warned not to try to bring their shellfish over to France for the next few days, the PA news agency understands.
Further talks between France and the UK are expected on Thursday as the post-Brexit dispute continues.
It comes as Jersey’s minister for external relations called on France to remove its threats of retaliation altogether.
Skipper Phil Channing, who has fished out of Jersey for 48 years, said the current situation following Brexit was “absolutely disgusting” and is driving fishermen out of the industry.
He told the PA news agency: “The whole situation’s so unfair.
“One of my mates, he’s been doing it 40 years – he’s thrown in the towel.”
Mr Channing, who owns the 20ft Vanden Plas fishing boat, spoke after bringing in about 300kg of scallops on Tuesday afternoon with his son.
The shellfish were hoisted up to the quayside and handed over to local exporters ready for sale.
Mr Channing spoke of the difficulties faced by the island’s fishermen who can no longer take catch straight into France’s ports like their French counterparts, instead having to go via Jersey for checks.
He told PA that the Jersey government has the power to ban fishing in its waters between three and 12 miles offshore.
He added: “We have all got together and said if they don’t start being fair we are going to call on the Government to do it – close the whole fishery down.
“We can’t land them there (in France) anyway”.
He said the additional hassle following Brexit is a “total nightmare” and has roughly halved his output.
Mr Channing added that he would “like to see England take us over to be honest”, in reference to the fishing fleet.
The last four generations of Mr Channing’s family have been fishermen, including his son, father and grandfather.
But he added: “I don’t think there will be a fifth.
“It’s pretty sad, the whole affair.”
Earlier on Tuesday, Jersey’s minister for external relations welcomed the continued talks but called on France to remove threats of retaliation altogether.
He told PA: “We agree that we should sit down and continue to look at the evidence, but it would be far better, and we call upon the French, to remove those threats altogether and so that they wouldn’t implementing counter-measures.
“Because at the end of the day it’s in the interests of the Jersey fishing community, it’s in the interests of the Norman fishing community, and it’s in the interests of the Breton fishing community that Jersey’s waters are managed in a sustainable fashion for the future.
“It’s in their best long-term economic interests not that we just issue licences because there’s a political will, and somebody would like a licence, but that they meet the terms of the trade deal.”
Over in Granville in France, trawler owner Samuel Deshayes told The Associated Press: “We don’t know what to expect. We learn new things every day”.
Asked about the row over fishing licences, he added: “Jersey — I don’t know why they are causing problems. Even the English don’t quite understand why Jersey is resisting.”