About 140 firefighters responded to the scene at 1:30 a.m. but were unable to stop the blaze until 7:30 a.m., Radio France Internationale said.
The fire spread quickly because the building was empty for renovations, firefighters said.
Artwork in the mansion, including work by Le Brun who decorated parts of Versailles, may have been damaged by the flames and smoke or water that was used to put out the blaze.
The mansion, the Hotel Lambert, was designed by Louis Le Vau, who later became King Louis XIV's principal architect.
It was built in the 1640s and is now owned by a Qatari Prince Abdullah bin Abdullah al-Thahi, RFI said.
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