Kieran Knight's body was found by a fisherman on Oceane beach, near where he disappeared on Messanges beach, the source said, confirming a report in the newspaper Sud Ouest.
The teenager had disappeared while swimming with his father on Wednesday afternoon, apparently after he was caught by a strong undercurrent and unable
to get back to shore.
Three helicopters and a patrol boat were initially deployed in an attempt to find the teenager, France's Atlantic maritime authority said. Searches continued on Thursday and Friday.
At the time of the tragedy, witnesses said the boy had been carried under the water, according to police.
The Aquitaine coast where the tragedy occurred is considered to be particularly dangerous because of a strong "undertow", which can carry away swimmers.