The deaths occurred on Tuesday after an overcrowded small boat carrying about 110 people set out to cross one of the busiest shipping lanes in the world.
The French coast guard was still searching for any survivors.
Five people have died trying to cross the English Channel from France in an overcrowded boat. (AP PHOTO)
"A tragedy occurred on a boat overloaded with migrants early this morning" local prefect Jacques Billant told reporters.
"We deplore the deaths of five people, a seven-year-old girl, a woman and three men.
"The engine stopped a few hundred meters away from the shore and several people fell into the water."
Rescuers had arrived quickly and picked up 47 people, he said.
Four were taken to hospital but their lives were not in danger.
"Another 57 people stayed on board," he said.
"They did not want to be rescued.
"They managed to restart the engine and headed towards Britain."
The boat had left from Wimereux, about 32km southwest of Calais.
A British border force boat carrying more than 20 migrants in life jackets was seen off the coast in Dover, southern England, about 32 km from French shores.
It was not clear where these migrants had set out from.
The attempts to cross the Channel took place hours after Britain's parliament passed legislation that will allow the government to send asylum-seekers to Rwanda rather than stay in Britain for processing.
Start the flights.— Rishi Sunak (@RishiSunak) Stop the boats.That's what this bill delivers. pic.twitter.com/y93Ti3qe2kApril 23, 2024
Stopping the flow of migrants is a priority for British Prime Minister Rishi Sunak's government, which says the Rwanda plan will act as a deterrent.
Human rights groups and other critics say it is inhumane.
"These tragedies have to stop," Britain's interior minister James Cleverly said of the latest migrant deaths at sea.
Sunak, speaking after the bill passed in parliament, said the focus was now on getting flights to Rwanda off the ground.
The bill is expected to receive Royal Assent this week, meaning it has passed into law, and Sunak has said he expects flights to depart within 10 to 12 weeks.
"I am clear that nothing will stand in our way of doing that and saving lives," he said in a statement.
Asylum seekers - many fleeing wars and poverty in Africa, the Middle East and Asia - started arriving in small boats on the English coast in 2018.
More than 6000 have arrived in Britain already this year, a rise of about a quarter on the same period in 2023.
The worst incident came in November 2021 when 27 migrants perished when their dinghy capsized near Calais.
The Channel is one of the world's busiest shipping lanes and currents are strong, making the crossing on small boats dangerous.
The people smugglers typically overload the boats, leaving them barely afloat and at risk of being lashed by the waves as they try to reach British shores.
The first deportation flight to Rwanda in June 2022 was blocked by European judges.
Britain's Supreme Court then upheld a ruling that the scheme was unlawful because migrants were at risk of being sent back to their homelands or to other countries where they would be at risk of mistreatment.
