Macduff Shellfish’s scallop vessel Cornelis Gert Jan was ordered to divert to the port of Le Havre after France said it was fishing in its waters without a licence.
The French said that another British trawler had been fined for obstruction after refusing to allow police to board to carry out checks.
The incidents came amid anger in France after the UK and Jersey turned down applications from dozens of French boats to fish in their waters.
It said that was a breach of Britain’s post-Brexit trade deal with the EU.
French ministers have warned they will block British boats from some French ports and tighten checks on vessels travelling between France and the UK if the issue is not resolved by Tuesday.
Sustainable fishing campaigners Open Seas said Cornelis Gert Jan was one of the world’s largest scallop dredger so it was not surprising the France were upset by its presence in what it described as “extremely damaging” type of fishing.
The 328-tonne boat is 36m (117ft) long – three times the length of an average British trawler.
Open Seas policy director Phil Taylor said he did not think the boat was operating illegally, but France may have acted in frustration at the scale of its dredging when its boats had been refused licences to fish in UK waters.
He said scallop dredging was not well regulated and there were no catch quotas.
UK Environment Secretary George Eustice said the French threats appeared to breach international law and warned the UK would respond in an “appropriate and calibrated” manner if they were carried out.
Macduff Shellfish, based at Mintlaw in Aberdeenshire, said the vessel had been fishing legally in French waters.
Andrew Brown, its director of sustainability, said: “It appears our vessel has been caught up in the ongoing dispute between the UK and France on the implementation of the Brexit fishing agreement.
“The Cornelis does have catch aboard.
"This may be confiscated by the French authorities unless a speedy resolution is achieved.
“We are looking to the UK Government to defend the rights of the UK fishing fleet and ensure the fishing rights provided under the Brexit fishing agreement are fully respected by the EU.”
Mr Eustice said the vessel had been granted a licence by the EU but that there were reports that it subsequently had been removed from the list of vessels permitted to fish in French waters.
France’s Europe minister Mr Beaune said: “We have been extremely patient…our fishermen have been extremely responsible.
“And so, from November 2, it’s over.
“Now we need to speak the language of force because, unfortunately, that seems to be the only thing this British Government understands.”
French maritime minister Annick Girardin said Britain’s “failure to comply” with the Trade and Co-operation Agreement (TCA) is “unacceptable”.
“We have fishing rights, we must defend them and we will defend them.”
The dispute comes five months after two Royal Navy vessels were sent to Jersey after an attempted French blockade of St Helier by French fishing boats over fishing rights in which France also threatened to cut its electricity supplies.