Bozon is married to Hélène Barbier, who was an alpine skier. They have three children, sons Tim and Kevin, and daughter Allison. Both Tim and Kevin play professional hockey; Tim is with Genève-Servette HC of the National League and was selected by the Montreal Canadiens in the 2012 NHL Entry Draft, while Kevin is currently with EHC Winterthur of the Swiss League. Bozon's father, Alain Bozon, was also a hockey player, and was elected into the French Ice Hockey Hall of Fame in 2012.