"We are ready to use these retaliation measures," Annick Girardin, the maritime minister, told lawmakers in the French parliament. "I am sorry it has come to this. We will do so if we have to."
Ms Giradin mentioned the underwater cables that supply Jersey, the largest of the Channel Islands, with about 95 percent of its electricity and suggested they could be shut down. The remaining five per cent of its electricity is provided by on-island diesel generators.
The self-governing British Crown Dependency would face all-island power cuts if the French threat was carried out. There were three island-wide power cuts in six years until a new £40 million pound, 16.7-mile cable was laid between Jersey and France in 2016.
On Friday, the UK authorised 41 ships to fish in waters off Jersey. The French fisheries ministry said this was accompanied by new demands "which were not arranged or discussed, and which we were not notified about".
The new measures set out "where the ships can go and cannot go", as well as the number of days the fishermen can spend at sea and using what machinery, the ministry claimed.
"This is absolutely unacceptable," Ms Girardin said. "If we accept this for Jersey, it would imperil our access everywhere."
David Jones, the deputy chairman of the European Research Group of Tory MPs, told The Telegraph: "This is straightforward demanding money with menaces, which is not the way a 21st century democratic country behaves. The simple fact is this is bullying in order to get the UK to back down on fishing."
Lord Frost, the Brexit minister and former UK negotiator, was set to meet Clément Beaune, France's Europe minister, for previously planned talks on Tuesday night. In late April, Mr Beaune said Paris would block any EU decision granting the City of London access to the Single Market unless the UK met its fishing commitments.
Britain and France have clashed over fishing rights several times in recent weeks. On April 23, French fishermen blockaded lorries carrying British catch and accused the UK Government of dragging its feet over the issuing of licences to small French vessels in the 6-12 nautical mile zone.
Under the terms of the UK-EU Brexit agreement on fishing, EU boats can fish within the zone if they have evidence of historical fishing activity from 2012-2016. While this is not a problem for larger boats, many smaller ones do not carry the necessary electrical equipment.
A spokesman for the Department for Environment, Food and Rural Affairs said Jersey was responsible for its own territorial waters and fishing management in them, but the UK was responsible for the international relations of the Crown Dependencies.
"We have been working closely with the EU and the government of Jersey on fisheries access provisions following the end of the transition period for licensing," the spokesman added.
The Jersey government could call on the UK to enforce its rules if it wished, but no request has yet been made.
The island's government said it had issued licences in line with the UK-EU Trade and Cooperation Agreement and that the rules meant licences could be issued if there was data proving EU boats had previously fished in its waters.
It said France and the EU 's complaints were taken "very seriously", but the Jersey government had acted in good faith and on legal advice.
The dispute comes as UK and EU negotiators remain locked in discussions over the annual catch quota for the more than 100 different shared fishing stocks. The UK wants to increase the catch of haddock and cod in Scotland by redeploying quota from other better-stocked areas in the UK such as the North Sea.