He was taken to the hospital to be treated for shock and has not been arrested or charged.
The victim's body will now undergo an autopsy to determine the exact cause of death.
Dozens of gendarmes surrounded the area where the tragedy happened, as others attempted to contact the victim's next of kin.
Antonia Chapple, who is originally from Dorset but has lived in Morzine for 17 years, shared the same friendship group as Mr Sutton and told Sky News: "Locals do feel nervous, and often wear brightly coloured jackets both for themselves and their dogs, when out walking".
It is the latest in a serious of shooting tragedies involving innocent passers-by being killed or severely wounded during France's hunting season, which started last month.
He was reportedly wearing bright clothing as he cycled through a well-known course. "He now faces trial and prison".
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The hunter, who has also not been indentified, is being investigated for "aggravated manslaughter".
And in September 2017, a 13-year-old boy was apparently mistakenly shot dead by his grandfather during a hunting trip near the village of Triaize.
According to the Guardian, "The accident came barely two weeks after another young hunter in the region was sentenced to a year in jail for involuntarily killing a trail runner with a single bullet to the head, prompting widespread calls for tighter restrictions to be imposed on hunting in areas popular with the public".
In November, a deer hunter who was just about to get married was gored to death by a cornered deer who charged him with his antlers in a wood near Paris.
Mr Sutton's death is the latest in a series of fatal shootings involving hunters in France in the past year.