Kammala jumla mai zuwa: An haifi Bozon a St. Louis, Missouri, inda mahaifinsa, Philippe Bozon, ya buga wasan hockey na St. Louis Blues na National Hockey League (NHL), amma ya girma a Faransa, inda mahaifinsa ya fito. Daga nan Bozon ya koma Switzerland don ci gaba da aikinsa, kafin ya koma Kanada bayan Kamloops Blazers ya zaɓe shi a cikin 2011 CHL Import Draft. A cikin
2012 NHL Entry Draft, Bozon ya zaba 64th gaba ɗaya ta Canadiens. A lokacin kakar wasa ta uku tare da Blazers Bozon ya yi ciniki zuwa Kootenay Ice. A duniya Bozon ya taka leda a tawagar matasa ta Faransa a gasa da yawa kuma ya shiga cikin manyan 'yan wasan Faransa a gasar cin kofin duniya ta IIHF ta 2013. Bozon ya kamu da cutar meningococcal mai barazanar rayuwa a farkon shekarar 2014, kodayake daga karshe ya warke.