Laurent Camprubi fired a flare after his boat, the Jeanne Solo Sailor, ran into trouble at around 8:30 pm on Monday when it was 14 miles (22 kilometres) from the Sisargas Islands off Spain's northwestern Galicia region, Spain's maritime rescue service said Thursday in a statement.
A rescue ship and three helicopters were immediately dispatched and the search team found the boat overturned in the darkness, it added.
In a video shared by the service, a rescuer can be seen being lowered onto the ship's hull and crouching over it, appearing to bang on it before listening for signs of life.
Camprubi began knocking from inside and crying out for help but due to the rough seas the rescuers had to first prevent the ship from sinking further and waited until morning to get him to safety.
"I knew they were there but I had to hold on. I thought of my wife, my children. I told myself that I would hold on for them. I could not abandon them," he said.
"When I heard the diver it was a great relief but then there was a whole operation that took time because conditions were difficult."
Spain's maritime rescue service described the operation to save Camprubi as "verging on the impossible".
First rescuers attached buoys to the capsized ship's hull, and the following day two divers equipped with torches swam under the boat to look for Camprubi, the coast guard statement said.
When the divers spotted him they extended a pole towards him which he immediately grabbed.
"He rushed towards us... we pulled him to the surface," the statement said.
Once he got to the surface, Camprubi said he hugged his rescuers before he was airlifted to hospital by helicopter for checks.
"These are moments which I will never forget," he said.
While Camprubi's body temperature was just 34.5 degrees Celsius when he was rescued and he was very dehydrated, he escaped uninjured.
He said his boat capsized in just a few seconds and then began to sink.
"The water continued to come in little by little and the electronic equipment of the ship tore off," Camprubi said.
"It was getting more and more dangerous to move around so I crouched down in a corner and waited, hoping for help to arrive."
Camprubi -- an experienced sailor who has won several regattas -- said at first he had an air bubble of about 80 centimetres that allowed him to breathe but "this spece was slowly shrinking".
"I understood that my hours were numbered," he added.
The maritime rescue service said that when Camprubi was brought to the surface at around noon on Tuesday, he had "just 30 centimetres (12 inches) of air". It said he had spent 16 hours under the boat.
Juan Ferrer, head of the rescue operations, said the neoprene suit Camprubi was wearing prevented him from getting hypothermia.
He also praised the French sailor for "calmly awaiting our arrival".
Camprubi, who had set sail from the Portuguese capital Lisbon on Sunday morning, said he expects to be reunited on Thursday in Spain with his wife and children.
"I am going to continue to sail," he said.
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