Stephen Jones is putting together a useful movement history for the shroud beginning in 1355:
Montfort (c.1358-1359). In 1358, following the French defeat at the 1356 Battle of Poitiers in which Geoffroy I died, marauding bands of English soldiers attacked French towns, including nearby Troyes. So Jeanne probably took her young son Geoffroy II de Charny (1352–1398), and the Shroud, from Lirey south to the comparative safety of her castle atMontfort-en-Auxois.
[ Left (enlarge): Montfort-en-Auxois castle:Burgundy Tourism. ]
Anthon (c.1359-1388) . In c.1359 Jeanne married the wealthy Aymon IV of Geneva (c. 1324-1388) and took Geoffroy II and the Shroud from Montfort to one of Aymon’s estates in High Savoy (that part of France bordering both Switzerland and Italy), probably Anthon.
[ Right (enlarge): Chateau at Anthon built in 1315 by Guichard d’Anthon, presumably Aymon IV’s great uncle Guichard VI d’Anthon (c. 1278-1320), which Aymon inherited through his mother Isabelle d’Anthon (c.1307-1335). Presumably Jeanne, Geoffroy II and Aymon IV lived here with the Shroud for ~29 years between 1359 and 1388. ]