Officials said the cathedral's organ was destroyed and its platform could collapse, but added that the damage was not comparable to last year's fire at Notre-Dame Cathedral in Paris.
Fire crews were alerted just before 08:00 am (0600 GMT) to the blaze at the Cathedral of St Peter and St Paul and around 100 personnel rushed to the scene.
After two hours, emergency teams managed to contain the fire at the gothic structure, built between 15th and 19th centuries, said regional fire chief General Laurent Ferlay.
Prime Minister Jean Castex said he would visit the scene later on Saturday.
“I want to know what happened but first I'm going to show my solidarity with the people of Nantes,” Castex told reporters.
President Emmanuel Macron tweeted his “support for our firefighters who are taking all the risks to save this gothic jewel”.
The building was last hit by fire in 1972. Its roof took more than 13 years to repair.
Another religious building in Nantes — the Basilica of St Donatian and St Rogatian — was struck by a fire in 2015 that destroyed three-quarters of its roof.
In April last year, a fire engulfed Paris's 13th century Notre-Dame cathedral, causing its steeple to collapse and sending billowing fumes containing toxic molten lead into the air. The structure will take years to repair.
Un incendie est en cours à la Cathédrale de Nantes
Les pompiers tentent de maîtriser les flammes ⤵ pic.twitter.com/wgSEdDOioX
— BFMTV (@BFMTV) July 18, 2020