Béatrice Marguerite de Faucigny

c.1135 could be the date of birth

PLZ attention to Beatrice de Vaupergue who seems to come only from Wiki ENG very light Draft anyhow childless *https://en.wikipedia.org/wiki/William_I_of_Geneva (FR better)

-http://fmg.ac/Projects/MedLands/burgkgenev.htm#BeatrixFaucignyMGuil...
6. BEATRIX . "Willelmus…Gebennensis comes" founded the Chartreuse monstery of Pommiers, with the consent of "Humbertus filius meus…B. quoque uxor mea et filius meus Aymo quinquennis", by charter dated 1179[400]. Her parentage is confirmed by the Chronicle of Alberic de Trois-Fontaines which names her daughter "Margareta filia domni de Fusceneis de matre Guilelmi, filii Humberti comitis Gebenensis" as wife of "comitis Thome de Sabaudia"[401].

m as his second wife, GUILLAUME de Genève, son of AMEDEE [I] Comte de Genève & his first wife Mathilde de Cuiseaux ([1131/37]-25 Jul 1196). He succeeded his father in 1178 as Comte de Genève.