The 75-year-old set off two distress signals on Thursday night, which were picked up by French, Portuguese and American sea relief services, his daughter wrote on social media on Saturday.
“Of course we are very worried,” she said, in wait of news concerning her father’s whereabouts.
Portuguese officials discovered an upturned vessel off the Azores coast. Savin’s body was found “lifeless in a cabin” by a diver sent by the country’s maritime officers.
The circumstances of his death have not yet been determined.
In a statement posted on Facebook, his team said: “Unfortunately, this time the ocean was stronger than our friend, who loved sailing and the sea so much.”
The French former paratrooper, who also worked as a pilot and park ranger, posted on Wednesday that he was contending with solar power difficulties and strong winds.
He said, at the time, he was “not in danger”, despite it costing him “physical energy”.
Jean-Jacques Savin made the 2,800-mile long journey in a barrel in 2019, before setting off again on 1 January 2022 to row across it.
Mr Savin’s first trip was apparently partly inspired by a trip taken by Alain Bombard, who crossed the Atlantic in an inflatable boat in 1952.
Mr Bombard survived by living only on fish and plankton found on the way and wrote a book about his journey.
According to Sky News, he hoped to reach the Caribbean in the eight metre-long rowing boat.