Rocks, smoke bombs and other projectiles were allegedly hurled at English and Scottish vessels during the confrontation in the early hours of Tuesday morning.
Around a dozen British boats were targeted by the rival flotilla in a protest over fishing rights in the scallop-rich waters.
The Government said it had contacted officials in France about the matter, adding the vessels were “legally entitled” to fish in the area.
The South Western Fish Producers Organisation, which represents many of the boats and has been negotiating with French fishermen, condemned the behaviour as dangerous.
Chief executive Jim Portus told the Press Association: “They are endangering life at sea by being unprofessional.
“The French might look like heroes to the French coastal communities but it’s really awful to put other mariners in danger.”
Around 40 French boats were said to be responsible for the disruption.
One of the British ships, The Golden Promise, had a window smashed by an airborne can, while another suffered fire damage after a flare was thrown at it, Mr Portus said.
He claimed to have received a message from the chief negotiator of the French scallop industry on Wednesday morning that said: “I regret the altercations that occurred... it will not happen again.”
Maritime authorities in France also sought to soothe tensions on Wednesday morning, decrying the showdown as “very dangerous” and expressing hope that “things will calm down”.
The long-running dispute centres on a section of the Channel from which French fishermen cannot harvest scallops until later in the year, due to domestic environmental laws.
Dramatic footage broadcast by France 3 Normandie showed boats colliding as tensions finally boiled over.
One of the British boats involved in the clash was said to be the Honeybourne 3, a Scottish scallop dredger, along with two ships from Brixham harbour, The Golden Promise and Joanna C.
Fears have been raised about the safety of the British fleet going forward, which the Government said was its “highest priority”.
Sheryll Murray, MP for South East Cornwall, claimed Environment Secretary Michael Gove had assured her that “appropriate measures” were in place to protect fishermen.
She also criticised the response of the French authorities, saying there was “no evidence whatsoever” that they had taken action against the vessels.
Dimitri Rogoff, head of a Normandy fishermen’s association, said the violent scenes “demonstrate the exasperation of Normandy fishermen in a situation which persists and does not change”.
But it is not the first time such an encounter has taken place, according to the owner of one of the Brixham boats.
Derek Meredith told the BBC: “It’s happened in previous years, two years ago it happened to us - not as forceful as this time I wouldn’t have said - but the same thing, the French navy were there on site and never done a thing.
“We reported it to the (Marine Management Organisation), nothing happened, it just went on deaf ears.”
The skipper of Joanna C, Nathan Clark, also told the broadcaster: “I’m not really concerned because we’re doing nothing wrong... it’s just the safety of my crew and the boat really, because there’s nothing to stop them doing it all over again.”
Britain’s National Federation of Fishermen’s Organisations has appealed for calm, while the Scottish White Fish Producers Association lashed out at the “vigilante behaviour”.