The paper cited a new report which claimed that his co-pilots were also dangerously tired.
Three Irish nationals were among the dead when Air France flight 447 fell out of the sky as it travelled from Rio de Janiero to Paris in June 2009.
The Airbus A330 had rolled from side to side during a tropical thunderstorm, and co-pilots 32-year-old Pierre-Cedric Bonin and David Robert 37, were unable to bring the plane under control.
When Marc Dubois, the 58-year-old captain returned from a break his deputies were panicking so much they were allegedly unable to tell him what the problem was.
The planes two black box flight recorders indicated that the airspeed sensors malfunctioned, probably because they had frozen up.
But according to the Daily Mail a further recording of Dubois has emerged in which he says: 'I didn’t sleep enough last night. One hour, it’s not enough.' According to the new report Dubois was already ‘grumbling’ less than an hour and a half into the flight.
The pilots had reportedly spent the night before in Rio with their wives and girlfriends, and the new report infers they may not have been alert enough the next day to deal with a high-altitude stall, because they ignored normal procedures and raised rather than lowered the plane's nose when it lost lift, or stalled.
The result was a terrifying three-and-a-half minute plunge before hitting the ocean. All on board died after the plane hit the sea at a speed of 180 feet a second.
The French aviation safety authority has already ruled that the 'captain failed in his duties' and 'prevented the co-pilot from reacting appropriately.'
Meanwhile French judges have launched a criminal inquiry into Air France and Airbus for alleged manslaughter. Those on board included Bonin's 38-year-old wife Isabelle, who was traveling without their two boys, aged eight and four.
A judge has already ordered Air France to pay around $180,000 in compensation to the families of each victim, but this figure is almost certain to rise.
Responding to the reports and rulings Air France has reportedly reviewed and improved its training procedures since the crash.