April 15th, 2019: Notre-Dame Cathedral in Paris was burning, the spire collapsed on the nave, vaults crumbled and most of the timber roof was gone. In the post-disaster context, the authenticity and the monitoring of the archaeological remains are crucial for their potential reuse during reconstruction. This paper analyzes the collapsed transverse arch from the nave of Notre-Dame as a case study of reconstruction, using the digital twin framework. We propose four facets for the digital twin experiment—physical anastylosis, reverse engineering, spatio-temporal tracking of assets, and operational research—that are described in detail, while being assembled to support a hybrid reconstruction hypothesis. The digital twin can realize the parallel unfolding of physical-native and digital-native processes, while acquiring and storing heterogeneous information as semantically structured data. The results demonstrate that the proposed modeling method facilitates the formalization and validation of the reconstruction problem and increases solutions performances. As result, we present a digital twin framework application ranging from acquisition to data processing that informs a successful hybrid reconstruction hypothesis.