Billionaire François-Henri Pinault, chairman and CEO of the Kering group that owns the Gucci and Yves Saint Laurent fashion brands, has already pledged €100m (£86m; $113m) towards rebuilding Notre-Dame, AFP news agency reports.
The French charity Fondation du Patrimoine is launching an international appeal for funds for the cathedral, a Unesco World Heritage site.
The fire started at around 18:30 (16:30 GMT) on Monday and quickly reached the roof of the cathedral, destroying its stained-glass windows and the wooden interior before toppling the spire.
Firefighters then spent hours working to prevent one of the iconic bell towers from collapsing. Search teams are now assessing the extent of the damage.
Sections of the building were under scaffolding as part of the renovations and 16 copper statues had been removed last week. Work began after cracks appeared in the stone, sparking fears the structure could become unstable.
Mr Macron said the cathedral was "for all French people", including those who had never been there, and praised the "extreme courage" of the 500 firefighters involved in the operation.
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