The 34-year-old, named locally as Marc Sutton, was killed by a stray bullet while riding in woodland near Montriond, close to the Swiss border.
He was biking on a popular mountain track when he was shot by a 22-year-old who was taken to hospital in severe shock.
Originally from Caerphilly, south Wales, he owned a restaurant in the small town of Les Gets.
The Foreign Office said it was in touch with local authorities and was providing support to his family.
Mr Sutton, a keen snowboarder and mountain biker, ran a private catering business in the area and opened his own restaurant, Wild Beets Kitchen, earlier this year.
In a Facebook post, he said of the restaurant: “I still can’t believe that this is ours! Hard work does pay off and dreams do come true.”
Philippe Toccanier, prosecutor for the Thonon-Les-Bains region, told the Associated Press (AP) the death in thick woods was believed to be an accident.
But he said that Mr Sutton “couldn’t be confused with game, as he had a coloured helmet and a coloured mountain bike”.
In the past three years, more than 20 people have died in hunting accidents in France.
On a local Facebook group people expressed horror and discussed how to prevent further incidents.