The article seems to agree with your comment:
> "It [Enedis] said it was able to isolate sections of the network to supply priority customers, such as hospitals, key industrial installations and the military and that it was up to local authorities to add telecoms operators infrastructure to the list of priority customers."
This is also a good argument for mesh-networks between cell phones independent of cell towers, although those don't scale for large numbers connected phones and large numbers of users. Texting could be supported via such mesh-nets easily I imagine, but not video.