Speaking outside a hospital in Calais, Darmanin said the dead included five women and a young girl. He said two were rescued and one was still missing.
French President Emmanuel Macron and British Prime Minister Boris Johnson have expressed their condolences to the families of the victims.
Macron said his country would not allow the English Channel to become a graveyard and urged its European counterparts to step up efforts to avoid future tragedies.
“I would like to express my unconditional support and sympathy to the families of the victims and their loved ones,” the president said in a statement.
“I assure them that responsible individuals, a network of traffickers who exploit misery and crisis, endanger human lives and ultimately destroy families, will do everything possible to find and condemn,” he added.
Macron said France had been working with Britain for months to dismantle the smuggling network.
He said that since the beginning of 2021, 1,552 smugglers have been arrested along with 600 police officers and sex workers on the North Coast and 44 smuggling networks have been destroyed.
“Despite this action, 47,000 attempts have been made to move to Great Britain since January 1. Our rescue services have rescued 7,800 migrants.”
The country’s maritime minister, Enik Girardin, said French, British and Belgian helicopters were searching for the missing.
French Prime Minister Jean Costa has called the incident a tragedy. “My thoughts are with the many missing and injured, the victims of criminal trafficking who exploit their pain and suffering,” he said in a tweet.
The Prime Minister of the United Kingdom Boris Johnson has said that he was shocked and saddened by the death at sea.
“My thoughts and sympathies go out to the victims and their families in the first place, and this is a terrible thing for them to suffer,” Johnson told reporters.
“But I also want to say that this outbreak underscores how dangerous it is to cross the Channel in this way. And it also shows how important it is for us now to step up our efforts to break the business model of sending thugs. So go to sea, and so on. It’s very important that we take action if we can do everything we can at our borders … so that we can separate the people who come here legally and the people who come here illegally. “
He added that the authorities would “leave no stone unturned in the business offerings of human traffickers and thugs … who are fleeing by literally killing.”
Johnson said it was time for Britain, France and Europe to “move forward” and work together. He was to chair a meeting of the Cobra Emergency Committee in response to the tragedy, his spokesman said.
UK Home Secretary Priti Patel said in a statement that the tragedy “serves as the most likely reminder of the dangers of these channel crossings organized by ruthless criminal gangs.”
He added: “We will intensify all cooperation with France and other European partners to prevent these deadly journeys for immigrants.”
On Monday, France’s interior ministry announced it had sent equipment and vehicles worth more than 11 million euros (. 12.3 million) as part of an agreement with the United Kingdom to “secure the 130-kilometer stretch of coastline, from Dunkirk to Somme Bay.”
It added that “police and gendarmes will have additional resources to complete the mission to fight illegal immigration.”
Last week, 243 people were rescued on the English Channel while trying to reach the UK.
So far this year, more than 25,700 people have crossed the English Channel in small boats to the UK, according to figures compiled by the UK’s PA Media News Agency. That’s three times the total for 2020, PA reports.
CNN’s Amy Cassidy and Joseph Ataman contributed to this report.