He added that rescue operations were underway to find two people still missing.
In a sign of the severity of the situation, Darmanin said he would travel to the site, near the town of Boulogne-sur-Mer, later in the afternoon.
Tackling illegal immigration has been a priority for both the British and French governments. More than 2,000 people have arrived in Britain on small boats over the past seven days, according to UK government figures, Reuters reported.
British interior minister Yvette Cooper called the death of the migrants a "horrifying and deeply tragic incident" and said the work to dismantle "dangerous and criminal smuggler gangs and to strengthen border security is ... vital and must proceed apace".
The Channel is one of the world's busiest shipping lanes and currents are strong, making the crossing on small boats dangerous. In August, two people were found dead after a boat carrying migrants trying to cross the Channel ran into difficulties.
MA/PR
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