Three people were killed in an attack near the Stade de France, with some reports suggesting a suicide blast.
Paris authorities have urged people to stay indoors.
Military personnel are being deployed across Paris.
Live: Follow the latest developments here.
In pictures: Paris shootings
Eyewitness accounts from the scene
The deadliest attack appears to have targeted the Bataclan concert hall. The BBC's Hugh Schofield says scores of ambulances have arrived at the scene, suggesting many victims inside.
Other attacks hit Le Petit Cambodge restaurant in the 11th district where a BBC reporter could see 10 people lying on the road, either dead or seriously injured. Another hit the nearby Le Carillon bar.
And an eyewitness told Liberation newspaper that he had heard more than 100 rounds being fired at a cafe in rue de Charonne. There are reports of up to six gunmen involved.https://www.rt.com/news/321883-shooting-paris-dead-masked/