Prosecutors say Paris police will conduct an investigation into "involuntary destruction caused by fire".
A major operation is under way to tackle the blaze, which broke out in the afternoon, and an area surrounding the building in central Paris has been cleared, it quoted officials as saying.
Photos and videos on social media show the roof of the Gothic building covered in flames, issuing a plume of smoke above the city.More news: Man arrested after boy falls from balcony at USA shopping centre
Macron tweeted: "Our Lady of Paris in flames". The emotion of a whole nation. "For French people, it's a national symbol", he said.
He recalled that Notre Dame bells sounded the death knell following the 2015 Paris attacks.
The peak of the church is undergoing a $6.8 million renovation project.
Soule and her father, Win Soule, 58, and Libby Heselton, 53, are on a weeklong trip to Paris where they planned to "see all the sights" and had just finished their visit to Notre Dame.
Paris mayor Anne Hidalgo described it as a "terrible fire" and urged people at the scene to stay safe.
There was still a risk that some of the interior structures could collapse, and firefighters would work overnight to cool them down, he said.More news: Stars gather for premiere in Belfast
Notre-Dame is in the midst of renovations, with some sections under scaffolding, while bronze statues were removed last week for works.
French President Emmanuel Macron arrived on the scene to meet with police and emergency responders, who were working to salvage artwork and artifacts inside.
Firefighters are attending to a large fire at the famous Notre Dame cathedral in Paris, France.
British politicians and religious leaders have expressed their sadness at the devastating fire engulfing Notre Dame cathedral this evening.
London Mayor Sadiq Khan has said his city "stands in sorrow with Paris today".
Paris Mayor Anne Hidalgo said on Twitter, "A bad fire is underway at Notre Dame Cathedral in Paris".More news: Dwyane Wade Gets Standing Ovation After Last Game in the National Basketball Association