During the fire in April 2019, part of the central vaulting of the nave of Notre-Dame de Paris collapsed beneath the impact of the fallen spire. The blocks composing the transverse arch were decontaminated, then subjected to archaeological examination prior to attempting to dry-mount them (i.e., without mortar) on the ground. The purpose was to collect as much information as possible about the arch itself (its state of conservation, geometry, fashioning of the blocks, assembly, etc.), to consider the possibility of putting the fallen stones back in their original places, and more broadly to improve knowledge about mediaeval cathedral vaulting. This article describes the method used during this mounting, which took place in winter 2020/21. Five criteria of differing kind and importance guided decisions on where to place the voussoirs, which way round to position them, and which to associate with which. Three were taken into consideration from the outset, with the interpretation of two of these changing over time: the non-standardized dimension of the voussoirs (their thickness), the presence of a cross mark on one of the joint faces, and the presence of rectangular notches on the extrados of the blocks for housing the end of a centering system for constructing the vault compartments. Two other criteria were incorporated as work progressed, pertaining to the order in which the blocks were collected after the fire, and the geological facies of the stones, thus introducing the idea of degree of confidence. By the end of this operation, only four blocks had been placed with certainty. Nevertheless, the criteria thereby defined and their weighting may now be used as a starting point for other investigation methods. In terms of archaeology, the observations carried out on this arch in these exceptional conditions suggest we should reconsider the dating of the nave vaulting, while throwing light more broadly on the relative chronology of building works on this landmark monument of Gothic architecture.