It's hard to overstate how hard this fire would have been to fight. That any of the structure was saved is testament to the skill and herculean efforts of the firefighters involved. If they had simply kept the fire from spreading to the buildings north of the cathedral, that would have been a "win".
It's clear from reports that the decision was made very early on to salvage what they could from the structure and set up to defend the western towers. The first fire streams put in place were in defense of the towers, not attacking the main body of the fire[1]. That was clearly the right tactical call, and trying to fight the fire head on likely would have resulted in the loss of the whole structure.
To highlight a few of the challenges...
The building itself had a huge amount of fuel (the tons of wood that have had centuries to dry), plus the significant amount of wood in the construction scaffolding supporting the renovation.
The fire likely burned undetected for some time in the attic space. By the time it was visible, it had a solid head start, and extinguishing it was never an option.
Once the fire was detected, getting sufficient manpower and equipment to the scene would have been the next challenge. The cathedral is on a small island, with limited access, and limited room to park vehicles in the vicinity. This would have been an "all hands on deck" fire, with off-duty staff recalled, but that takes time, and the initial incident had to be managed with relatively limited manpower (relative to the scale of the fire).
The next issue would be getting enough water to the scene. A fire like this requires tens of thousands of gallons of water per minute. There's likely only one or two water mains serving the island, which puts a hard cap on the amount of water that could be drawn from the local hydrants. The fact that it's an island obviously means there's a huge amount of water near by, but using that water has its own logistical challenges, as it requires special equipment (you can't 'suck' water through a soft fire hose), and special training. While I'm sure they had some capability to "draft" water from the river, it's not a skill that gets used often by urban fire departments, and it's likely not something they were set up to do in any significant way. In any large scale incident like this, there are often more firefighters working in "water supply operations" than there are actually fighting the fire.
Huge kudos to the firefighters on scene, and hopefully they'll have an opportunity for some well deserved rest in the coming days.
[1] https://twitter.com/shivmalik/status/1117864730453061634