Note that the Paris Fire Brigade is a branch of the Army [0] (and in this case, it shows).
Morals aside, it kind of make sense from an economical standpoint: a single guy dies, that's sad. A father of four dies, that's sad and the community has to support four orphans...
Controversial opinion: making that call to save living creatures is fine in my personal moral compass. Make that call for a building, be it symbolic and of rich cultural significance, not so much. As long as nobody is in danger, do everything to save it but if it burns to the ground, it can be rebuilt. A lost life and its consequences cannot.
I was, honestly, furious, when I heard the commander chose to send his men into the northern tower simply to save a pile of rocks....
[0]https://en.wikipedia.org/wiki/Marseille_Naval_Fire_Battalion
No one entered that building against their will. Quite the opposite, I'm sure (speaking from personal experience), the crews on scene would have been frustrated had they been told they had to stay out.
If it helps, consider it an extreme sport (in fact, firefighting is quite a bit safer than many sports). Firefighting often amounts to people engaging in what is arguably "optional" activities, for reasons that aren't necessarily clear from a purely rational standpoint. The actual reasons are a combination of many factors. There is certainly a desire to preserve property (especially when that property is irreplaceable), but there is also the adrenaline rush of working inside a burning structure, the camaraderie among the crews, etc.
If they are destroyed, they are lost to every future human being from now until the end of the universe. Even with time discounting, that's a great cultural loss. Should we risk lives to preserve historical & cultural heritage? Yes, absolutely.
If you're going to engage in reductio ad absurdum, at least be consistent and call the men "meatbags".
Thankfully the stakes are very rarely so high, and courage of this calibre is rarely called upon.