Prosecutor Pierre Sennes told journalists three fires had been started at the site and authorities were treating the incident as a criminal act. He gave no other details.
Dozens of firefighters brought the blaze under control after several hours. Smoke was still coming out of the Gothic structure after massive flames earlier engulfed the inside.
The blaze came just over a year after a major fire at the Notre Dame cathedral in Paris, which destroyed its roof and main spire.