The country and government being secular does not mean that the people left their Catholic roots behind. Atheist and religious French people share similar values and the past is very important to both.
To flip your point around, they'd save it because it's symbolically important. Same with the art in the Notre Dame.
I’ve literally been explaining that this whole time. Please try to read and comprehend things before issuing these vacuous replies.
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Edit: Someone on Reddit wrote a very interesting comment about its historical significance:
"Napoleon's coronation is incredibly recent in terms of Notre Dame's age. The amount of time between then and now represents less than 25% of the cathedral's existence.
It was built in 1163, one year after Genghis Khan's birth (or at least our best guess of his birth). Notre Dame predated Marco Polo and the founding of the Ottoman Empire by more than a century. It predates the creation of Islam. At the time of its construction, the best estimates for the global population are ~300 million (less than the current population of the United States). The cathedral was almost 200 years old when the Black Death destroyed a third of the world's population. The USA is currently younger than Notre Dame was when the Forbidden City was constructed in Beijing. It was 3 centuries old when Machu Picchu was built and Leonardo Da Vinci was born. It was over 400 years old when Shakespeare's Globe Theatre was built. It predated the original King James Version of the Bible by 450 years."
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Among other relics, a piece of the Crown of Thorns was inside the Cathedral. I don't have a hard time picturing someone braving a blaze to save that.
And we are talking a building that has survived the French history, the Revolutionaries didn't destroy it, the Communards didn't destroy it (and the destruction in this event were quite extensive http://paris1900.lartnouveau.com/paris00/commune_destruction...). It's a testament of the culture importance of the building and the fact it far exceeds its religious function.
Disclaimer: French and living in Paris (I've not seen the fire however).
Notre Dame is...was...a medieval Roman Catholic cathedral in a postmodern secular country, desecrated rather than revered by the revolutionaries who built modern France.