Chartres holds two things pilgrims still travel for that have nothing to do with how the building survived its own fires: a relic and a pattern on the floor.
The relic that paid for rebuilding
The cathedral treasury holds the Sancta Camisa, a length of silk cloth venerated since the early Middle Ages as the garment worn by the Virgin Mary at Christ's birth, a gift originally associated with Charlemagne's grandson Charles the Bald. When fire destroyed much of the earlier cathedral in 1194, the relic reportedly survived, an event read at the time as encouragement to rebuild, and donations tied to the relic's fame helped fund the Gothic cathedral that rose in its place within roughly thirty years, unusually fast for the period.
Walking the labyrinth
Set into the nave floor is a labyrinth, a single winding path roughly thirteen metres across dating to the cathedral's thirteenth century construction, of a design found at several other Gothic churches. Its original devotional use is not well documented from medieval sources directly, but the walked path has been revived in recent decades by pilgrims and visitors as a form of contemplative prayer, chairs cleared from the nave on set days specifically so people can walk it.
Two objects, two kinds of pilgrimage
The relic draws devotion tied to a specific claimed object; the labyrinth draws a walking practice tied to the path itself, and Chartres hosts both without treating either as more official than the other.