The friend, who said he was Sudanese, aged 16, was rescued on Tuesday night after the pair's small, inflatable vessel ran into trouble while trying to make their way to Britain from France.
He told police his companion, of the same age, had gone missing at sea, local authorities told AFP.
Hours later, a body was found on the beach in Sangatte in France's northern Pas-de-Calais region.
The body has not been formally identified, but local official Philippe Sabatier told AFP it was likely that of the missing boy.
“This unbearable tragedy mobilises us even more… against smugglers who take advantage of the distress of human beings,” Marlene Schiappa, France's minister delegate for citizenship issues, said on Twitter.
Immense tristesse: un adolescent de 16 ans, migrant soudanais disparu en mer cette nuit, a été retrouvé mort sur la plage de Sangatte ce matin.
Ce drame insupportable nous mobilise encore + avec @GDarmanin contre les passeurs qui profitent de la détresse d’êtres humains !
— ?? MarleneSchiappa (@MarleneSchiappa) August 19, 2020
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Since January 1st, authorities in northern France have recorded some 350 attempts or crossings involving more than 4,000 people, compared with 203 attempts and 2,294 people for the whole of 2019.
French maritime officials have rescued almost 1,000 people at sea attempting to cross the Channel in makeshift boats or even swimming, according to an AFP count.
The issue has been a source of tension in cross-Channel relations, with Britain accusing France of not doing enough to stop the crossings.
French authorities insist they are doing all they can.
On Friday and Sunday, rescuers plucked 38 and 31 people in small boats, including four children, from the Channel in small boats.