Notre Dame de Paris in flame

[Philippus Flavius Homovallumus]

Well shall have to see, but the latest images show that some of the vaulting in the nave has collapsed. Like most medieval Cathedrals Notre Dame's wooden roof rested on stone vaulting, the actual ceiling of the cathedral. The vaulting exerts an outwards pressure which is countered by the inward pressure of the flying buttresses. Once the structure is weakened by fire the vaulting can collapse, which means there's no counterpoint to the flying buttresses, leading to a risk of an inward collapse of the entire nave.

This sort of things can, of course, be countered by bracing etc. or (in an emergency) possibly undermining buttresses (although this could also cause the whole structure to twist and collapse. One possible bright spot here is that Notre Dame was already undergoing huge renovations which means there should be a Cathedral architect on-site with a thorough understanding of the structure and geometry of the cathedral.

The whole structure will take days to fully cool and settle, so it could be a while before we know the true extent of the damage. Between then and now there's nothing to do but hope and pray.