The Cornelis Gert Jan was detained at Le Havre amid a dispute over post-Brexit fishing rights.
The trawler operated by MacDuff Shellfish of Scotland is in and out of the port of Shoreham, in Hampshire.
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, head of public affairs for Macduff Shellfish, said the company was of the understanding that the captain of the Cornelis Gert Jan had been charged by French authorities.
“That’s the information we’ve received,” he told the PA news agency.
“The charge relates to fishing in French waters without a licence and that’s the bone of contention.
“We believe we were fishing with a valid licence and the French authorities don’t.”
Speaking to the BBC’s Good Morning Scotland programme on Friday, Mr Eustice said the scallop trawler was originally on a list of approved vessels but appeared to have been taken off, but was nevertheless entitled to fish in the waters.
He said: “We’re trying to get to the bottom of what happened.
“It is true that it was on the list originally and it had a licence.
“We understand that what happened is it may have made some changes to the engine on the vessel, and that meant that the licence had to be renewed.
“We’re trying to get to the bottom, working with Marine Scotland and the MMO and the owners of the vessel, to understand why it dropped off the list.
“But this is a minor administrative thing. I think it is entitled to fish in those waters.”
Mr Eustice added that France had decided to “politicise” the process of checking vessels this week saying French President Emmanuel Macron faced a difficult re-election challenge may be a “factor” in the fishing row.
Eustice accused France of “inflammatory language” and did not rule out blocking French vessels from landing their catches in the UK in retaliation.
“We will see what they do on Tuesday but we reserve the right to respond in a proportionate way.
“It’s always open to us to increase the enforcement we do on French vessels, to board more of them if that’s what they’re doing to our vessels, there are other administrative things we can require of vessels.”
Asked if the UK could block French vessels landing their catches in the UK, he said: “I’m not going to get into all the things we might do.
“If the French obviously do continue with this then yes we will take a proportionate response to that.”
The MP acknowledged that France detaining the British vessel may have been a “routine operation” but has received mainstream attention because French authorities last week “said they were going to introduce all sorts of problems and make life difficult for people”.
He also hinted that French President Emmanuel Macron facing a difficult re-election challenge may be a “factor” in the fishing row but Bruno Bonnell, a member of the French parliament who is in the same party as Mr Macron, argued that the row started over a lack of licences for France’s trawlers.
He said: “I don’t know, but there obviously is an election coming up in France, it may be that is a factor in this.”
UK ministers met on Thursday to consider the response, with the prospect of tit-for-tat action if France carries out its threats.
Brexit minister Lord Frost, who chaired the meeting, said: “I remain concerned by French plans on fisheries and beyond”, adding that “we expect to have more to say” on Friday.
The Government views the proposed actions as “unjustified” and questioned whether they were compatible with the UK-EU trade deal “or wider international law”.
A UK Government spokesman added: “We regret the confrontational language that has been consistently used by the French government on this issue, which makes this situation no easier to resolve.”
Asked about the claim by France’s Europe minister Clement Beaune told French TV news channel CNews: “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 UK-EU Trade and Co-operation Agreement (TCA) is “unacceptable”.
“It’s not war, it’s a fight,” she said.
“We have fishing rights, we must defend them and we will defend them.”
Foreign Secretary Liz Truss will challenge Paris’s ambassador to the UK Catherine Colonna on France’s intentions this afternoon after taking the rare step of ordering an allied nation’s envoy to be summoned.
Jim Portus, chairman of the Scallops Industry Consultation Group, told Sky News French authorities are being “extraordinarily over the top”
“The rules can’t be changed for France when they are applied to all the nations of the EU.
“So I think that France are being extraordinarily over the top in their treatment of British fishing vessels.”
Mr Eustice told MPs on Thursday 171 vessels have been licensed to fish in the UK six to 12 nautical mile zone, of which 103 are French, and 18 of those vessels are under 12 metres.