The scallop vessel Cornelis was ordered to divert to the port of Le Havre after the French authorities said it was fishing in French 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.
Diplomatic efforts to resolve the row have involved the UK’s ambassador in Paris, Menna Rawlings, and Cabinet minister George Eustice.
We are looking to the UK Government to defend the rights of the UK fishing fleet and ensure that the fishing rights provided under the Brexit fishing agreement are fully respected by the EU
Andrew Brown, Macduff Shellfish
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 in what Paris said 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.
Environment Secretary Mr 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.
He has been in contact with his French counterpart, while in Paris Mrs Rawlings has spoken to Europe minister Clement Beaune.
The owner of the Cornelis, Macduff Shellfish, said the vessel had been fishing legally in French waters and called on the British Government to protect the rights of British fishermen.
Andrew Brown, director of sustainability and public affairs at Macduff, 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 that the fishing rights provided under the Brexit fishing agreement are fully respected by the EU.”
In an emergency Commons statement, Mr Eustice said they were investigating what had happened.
He 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 for reasons that were unclear.
Now we need to speak the language of force because, unfortunately, that seems to be the only thing this British Government understands
France’s Europe minister Clement Beaune
Meanwhile Downing Street said it was continuing to seek talks with the French government and the European Commission to resolve the dispute over fishing licences.
The Prime Minister’s official spokesman said: “We are monitoring this situation very carefully. We have relayed our concerns to the commission and the French government.
“We think the threats outlined yesterday evening were disappointing, were disproportionate and were simply not what we expect from a close ally and partner.
“I can’t at this moment set out exactly what our response might be. It will be appropriate, it will be calibrated.”
Earlier, France’s Europe minister Mr Beaune told French TV news channel CNews: “We have been extremely patient… our fishermen have been extremely responsible.
“And so, from November 2, it’s over: we will engage in dialogue if the British want to, but we are taking retaliatory measures.”
We have fishing rights, we must defend them and we will defend them
French maritime minister Annick Girardin
He added: “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 also told French radio news programme RTL Matin that Britain’s “failure to comply” with the Trade and Co-operation Agreement (TCA) is “unacceptable”.
“It’s not war, it’s a fight,” she said.
“The French and the fishermen have rights. An agreement was signed.
“We must enforce this agreement. We have fishing rights, we must defend them and we will defend them.”
Mr Eustice said the UK has licensed 98% of EU vessels that have applied for access post-Brexit and more are expected to be granted following “constructive” talks with the European Commission.