I confirm what leons1701 just said, for the most part — I heard they didn't use blowtorches, due to the risks it would've represented in that particular environnment, but they may be other explanations: indeed renovating things is putting them at risk.
I've also read there were two distinct alarms. The first time the drill rang (during the mass), people climbed up there but they didn't see any fire or smoke, and they eventually ignored it, thinking it was a malfunction. People who left the cathedral came back into it. It rang again half an hour later and (if I understood correctly) this time it was too late to do anything, the whole frame was on fire. The firemen recognized the "Forest" was already a lost cause when they arrived, so instead of losing time even trying to save it, they divided themselves in two groups, one tasked with evacuating the artworks and the other tasked to containing the fire to that part and to deploy the needed equipments. It was a bold and, I guess, a difficult choice, but eventually it's probably what allowed to save the building and nine-tenths of the art pieces and relics.
A heads-up concerning the destructions and preservations, compared to what I wrote in my previous post (it's mostly good news):
- The "Mays" were actually removed during the operation. Apparently they partially suffered from soot but they have been taken to be restored by the teams of the Louvre Museum, this is the kind of things they know how to treat.
- The great organ received dust and soot too inside its pipes and machinery, so it would be unusable right now, but it was preserved both from the fire and from the water. It'll require a throrough and careful cleaning but there's no damage. The other, less large, organ that was on the ground wasn't so lucky.
- The rooster-shaped brass reliquary that was on the spire has been recovered. It's damaged, but not utterly destroyed, although there's no assurance yet of the state of the three relics (including a thorn from the crown of thorns) it was supposed to shelter.
- In the choir, the 18th century carved-wood stalls, the 18th group of statues, and the 19th century high altar, were apparently preserved (or mostly preserved with only minor damage).
- The Prime Minister launched an international contest yesterday, inviting architects to submit designs for replacing Viollet-le-Duc's spire, leaving open both the possibilities of a replica and of something new.
The President promised a rebuilding in the span of five years — probably with the 2024 Summer Olympics in Paris in mind. Some experts, though, are more wary, speaking of the possibility for such a work to extend up to decades.