The blaze blasted out stained glass windows and destroyed the grand organ in the 15th-century building in the city of Nantes on Saturday, officials said.
The incident is being treated as a criminal act, a prosecutor said at the scene. Pierre Sennes said three fires had been started at the site.
Images have shown smoke billowing from the cathedral, while a blaze lit up the building.
Residents and tourists watched aghast, and emergency workers cordoned off the area around the St Peter and St Paul Cathedral, which sits in the historical centre of Nantes, a city in western France.
Dozens of firemen brought the fire under control after several hours.
The fire had broken out behind the grand organ, which was completely destroyed, local fire chief Laurent Ferlay said.
Stained glassed windows at the front of the cathedral were blown out.
Mr Ferlay told reporters on Saturday morning more than 100 firemen were still at the site to ensure the blaze was completely under control.
However, the damage was not as bad as initially feared.
“We are not in a Notre Dame de Paris scenario. The roof has not been touched,” Mr Ferlay said.
The cathedral’s roof was destroyed by a fire in the 1970s, and was rebult 13 years later with a concrete structure to replace the ancient wooden roof.
“The fire of 1972 is in our minds, but at this stage the simulation is not comparable,” Johanna Rolland, the mayor of Nantes, said.