A tweet from Ginola's account said he had "never slept better" after his dramatic collapse while playing football on Thursday.
The 49-year-old former Newcastle and Tottenham winger was attending a celebrity golf tournament in Mandelieu on the French Riviera.
He was taken to the Monaco Cardio-Thoracic Centre, where he was operated on by Professor Gilles Dreyfus.
Speaking to the BBC, Dreyfus said onlookers had initially thought Ginola was joking, only to then be saved from becoming brain dead by someone performing CPR.
"David played a sort of charity football match. All of a sudden he collapsed and people thought it was a joke but after one or two minutes they realised it was serious," said Dreyfus, professor of cardiac surgery at the Monaco Heart Centre.
"Fortunately there was one person who had been trained in CPR, because otherwise he would have been brain dead. They then called the emergency services, who arrived eight minutes later with him in cardiac arrest.
"I was speaking to the captain and he was telling me the girl who was in the ambulance only knew where the football field, which isn't an official one but a private one, was because she had seen it that morning and asked somebody what it was.
"If she hadn't then most likely she would not have found it within the timeframe to save him.
"They arrived with him in cardiac arrest, he was shocked four times on site, they were able to restore a normal heart rhythm and within 10 minutes a helicopter arrived to transfer him to Monaco Heart Centre.
"I made the decision to transfer him to the operating theatre and he immediately underwent a quadruple heart bypass, which was very straightforward although difficult."
Dreyfus added that Ginola was "lucky" but was now recovering normally.
A tweet from Ginola's account then read: "Hello world, never slept better. I'm fine, just need to rest a bit. Thank you so much all of you for your magnificent support."
Ginola won 17 caps for France and also had spells at Aston Villa and Everton before his retirement in 2002.