Jersey says it is following the rules for issuing licenses set out in Britain's post-Brexit trade deal with the European Union.
Talks between island officials and representatives of the fishermen were not positive, said Hugo Lehuby, spokesman for the Normandy Regional Fisheries Committee.
"We're getting deeper into deadlock," Lehuby told Reuters. "Either this gets resolved, or retaliatory measures are taken."
British Prime Minister Boris Johnson, who led the 2016 Brexit campaign, had cast the trade deal as a way to take back control of the United Kingdom's destiny after Brexit.
On Thursday, he said the two Royal Navy vessels would remain off Jersey as a precautionary measure, according to his office. Jersey's government said Johnson had assured it of his unwavering support.
An official from the French presidency said the deployment of patrol vessels from both France and Britain was aimed at preventing clashes between trawlers on opposing sides of the row.
France is angry on April 30 Jersey issued 41 licenses with what the Paris government called unilaterally imposed conditions, including the time French fishing vessels could spend in Jersey's waters.
Jersey officials have said the accord stipulates licenses take into account how much time a vessel spent in Jersey's waters before Brexit.
The Europe Commission said that until further justifications had been provided by Britain, Jersey officials should not be attaching new conditions to the issuance of licenses.
"Full compliance with the TCA (Brexit trade deal) is essential in this process," Commission spokeswoman Vivian Loonela told a news briefing.
The fleet of about 50 fishing boats left the shores of Jersey, which lies 14 miles off northern France and 85 miles from Britain's southern coast, in the early afternoon. They had arrived at dawn, with some crew holding red flares aloft.
At least one French trawler entered the harbour and briefly blocked the Commodore Goodwill, a cargo vessel and ferry that connects the Channel islands to the British mainland.
The French presidency official said the deployment of patrol vessels spoke of France's concern and frustration.
Ship-tracking website marinetraffic.com showed the two British naval vessels, the HMS Severn and HMS Tamar, deployed on the south-western side of the island.
(Additional reporting by Tangi Salaun and Elizabeth Pineau; in Paris and John Chalmers in Brussels; Writing by Christian Lowe and Richard Lough; Editing by Mike Collett-White) ((email@example.com; +33 1 49 49 52 07))