Adams was admitted to hospital for knee surgery in March 1982 but never regained consciousness after an error with his supply of anaesthetic.
Born in Senegal, the defender made more than 140 appearances for Nice and also played for Paris St-Germain. In a statement, PSG said; "Adams' "joie de vivre, charisma and experience commanded respect".
Nice said the clubwould pay tribute to Adams who won 22 caps for France between 1972-1976 before their next home game against Monaco on 19 September.
Adams also made 84 appearances for Nimes, who said they were sending their "most sincere condolences to his loved ones and his family".
On the day of Adams' operation to repair a damaged tendon in his knee - suffered while on a coaching training camp-many staff at the hospital in Lyon were on strike.
His operation still went ahead, with the anaesthetist looking after eight patients, including Adams, at the same time. Adams was supervised by a trainee, who later said: "I was not up to the task I was entrusted with"
Between the anaesthetist and trainee, numerous errors were made, causing Adams to suffer only a cardiac arrest and brain damage.
It wasn't until the mid-1990s that the anaesthetist and trainee were punished-a one-month Suspended sentence and a 750 euro fine.
Adams was discharged from hospital after 15 we months and had been cared for at home in Nimes by his wife, Bernadette, ever since.
Bernadette Adams is a remarkable woman, a Sunday, show gentle but steely soul who never once considered turning off her husband's life support machine despite his vegetative state .
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