A police official said teams from three different police agencies are entering the monument to take samples and search for clues as to what caused the fire.
Police made a preliminary visit last week but were not able to conduct a thorough examination until the cathedral's structure was secured.
Officials believe the fire was possibly caused by a short circuit linked to renovation work under way before the fire.
The Paris prosecutor's office says all potential leads are being pursued.
The cathedral will remain closed to the public for years after the fire destroyed its roof and knocked over its spire.
Earlier this week, the French weekly newspaper Le Canard Enchaine reported how some scaffolding workers involved in the renovation had sometimes smoked on the site, despite a ban.
On Tuesday, Reuters news agency reported that the family owned Le Bras Freres scaffolding firm had ruled out a stray cigarette butt as a cause of the blaze.
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