A search operation began after another migrant was found with hypothermia on the shore at about 02:00 BST.
He told authorities that his friend, who could not swim, was missing after their makeshift boat capsized.
UK Home Secretary Priti Patel said the death of the young migrant was a “brutal reminder” that people smugglers exploit the vulnerable.
Bridget Chapman, of Kent Refugee Action Network, said that the government was wrong to focus only on the criminals organising crossings, adding that reports the boy had pushed off in a makeshift boat made it “likely that people smugglers weren’t even involved”.
She called on the Home Secretary to instead “turn her attention immediately to creating safe and legal routes so that no on else suffers the same fate”.
The Home Office would not confirm whether the boy had been trying to reach the UK.
Asked to clarify if there was evidence people smugglers were involved in the death, it said it would not comment on an investigation that is being lead by the prosecutors’ office in Boulogne-sur-Mer.