The French and British governments have been trying for years to stem the flow of migrants, who pay smugglers thousands of euros a head to cross from France to England aboard small boats.
A police source said the incident happened shortly after the boat was boarded.
Regional prefect Jacques Bilan will give a press conference at 10:00 local time, his office said.
Maritime authorities said on 14 September that numerous attempts had been made in recent days by migrants to cross the dangerous route in small boats, with 200 people rescued in just 24 hours on Friday and Saturday (13 and 14 September).
At least 12 migrants, mostly from Eritrea, died off the northern French coast when their boat carrying dozens of people capsized this month.
It was the deadliest such accident this year and increased the number of migrant deaths in the English Channel to 37, up from 12 in 2023.
According to British authorities, more than 22,000 migrants have arrived in England by crossing the English Channel since the start of this year.
British Prime Minister Keir Starmer and French President Emmanuel Macron pledged this summer to step up their cooperation in tackling the soaring number of undocumented migrants.
Crossing the English Channel often proves dangerous, and in November 2021, 27 migrants died when their boat capsized in the deadliest such accident ever.
French authorities are keen to stop migrants taking to the water, but do not intervene when they are on the surface except for rescue purposes, citing safety concerns. | BGNES