The man, who was not named, was attempting to beat the previous record of 55 shots in a bar in Clermont-Ferrand in central France on Friday.
“He swallowed around 30 glasses in the space of a minute,” a police source told AFP.
The man was driven home in a drunken stupor and emergency services took him in later that night.
He died the next day in hospital after falling into a coma and suffering a heart attack, his daughter, a 21-year-old student, told AFP.
The bar manager told local daily La Montagne that the man was drinking “much too fast” and he advised him to stop after the first 30 or so shots.
But the daughter disputed this version of events, saying it was only after the 56 shots had been consumed that he was told to go home.
“My father died by his own hand but it was the bar that served him the drinks,” she said.
She is waiting for the results of an autopsy carried out in the immediate aftermath.
The daughter said she would sue the bar if it transpired there was negligence in the case.
Police said the manager could be charged with “not assisting a person in danger.”
The manager himself said he was “very affected” by the death but declined to comment further saying he preferred to explain the events to officials.