More than 20 people are believed to have drowned after attempting to cross the Channel in an inflatable dinghy.
A fishing boat sounded the alarm earlier on Wednesday after spotting several people at sea off the coast of France.
The French AFP news agency has reported that five people have died while other French media have reported that five others were found unconscious.
Other reports suggest the death toll could be as high as 20.
French interior minister Gerald Darmanin confirmed on Twitter that people had died but did not give a number.
He expressed his horror at “the many deaths due to the capsizing of a migrant boat in the English Channel”, adding: “We cannot condemn strongly enough the criminal smugglers who organize these crossings.”
And French prime minister Jean Castex said the shipwreck was a “tragedy”.
“My thoughts are with the many missing and injured, victims of criminal smugglers who exploit their distress and injury,” he said.
The French maritime prefecture for the North Sea said that, shortly before 2pm on Wednesday, a fishing vessel had informed authorities of several people in the sea near Calais.
Both French and British authorities have launched a major search operation, with patrol boats and helicopters deployed.
French officials said: “The operation remains underway and several people have been rescued from the water. “(The French rescue service) has deployed maritime and aviation resources to search for others in the sea and evacuate those already located. Sadly, some of those rescued are in a life-threatening condition.”
More than 25,700 people have made the perilous journey to the UK this year – three times the total for the whole of 2020.
More to follow.