The 850-year-old Gothic building's spire and roof have collapsed but the main structure, including the two bell towers, has been saved, officials say.
Firefighters are still working to contain the blaze as teams try to salvage the artwork stored inside.
President Emmanuel Macron called it a "terrible tragedy". The cause of the fire is not yet clear.
Officials say it could be linked to the renovation work that began after cracks appeared in the stone, sparking fears the structure could become unstable.
Paris prosecutor's office said it had opened an inquiry into "accidental destruction by fire". A firefighter was seriously injured while tackling the blaze.
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