Daniel Roche, who is fascinated by air plane accidents and has spent years combing the Bossons Glacier looking for remains, made the discovery on Thursday.
“I had never found any significant human remains before,” he told AFP. This time however he had found a hand and the upper part of a leg.
In January 1966, an Air India Boeing 707 from Bombay to New York crashed near Mont Blanc's summit, killing all 117 people on board.
Another Air India flight crashed on the mountain in 1950, killing 48 people.
Roche said the remains he had found could be of a female passenger from the 1966 Boeing 707 flight, as he also discovered one of the plane's four jet engines.
Roche contacted local emergency services in the Chamonix valley who took the remains down the mountain by helicopter and they were due to be examined by experts.
“These remains are probably not from the same person,” said Stephane Bozon of the local gendarmerie.
“They are probably from passengers, but between the two aircrafts, it's difficult to say”.
Just 10 days ago, two bodies were found lying near each other, preserved in a receding glacier in the Diablerets massif in the Swiss Alps.
A DNA search identified the couple as Marcelin Dumoulin, a 40-year-old shoemaker at the time, and his wife Francine, a schoolteacher aged 37, who had disappeared in the Alps 75 years before.