A security official says the two brothers suspected in the Charlie Hebdo massacre came out firing, prompting the assault on the building where they had holed up with a hostage.
The official was not authorised to speak about the sensitive operations and spoke on condition of anonymity.
Officials say the brothers died in the assault.
Another official, police union representative Christophe Crepin, said it appeared that the gunman who took hostages at a kosher market had had also died in a nearly simultaneous raid there.
Security forces launched a major assault on the building late Friday afternoon.
A few minutes later, several people were seen being led from the kosher market in eastern Paris where another gunman had taken hostages.
Earlier, terrorists linked to each other seized hostages at two locations around Paris on Friday, facing off against thousands of French security forces as the city shut down a famed Jewish neighbourhood and scrambled to protect residents and tourists from further attacks.
By Friday afternoon, explosions and gunshots rang out and smoke rose outside a printing plant where two brothers linked to al-Qaeda and suspected in a newspaper massacre were holed up with a hostage north of Paris.
Security forces had surrounded the building for most of the day, cornering the suspects in the killings at the Charlie Hebdo newspaper in Paris. Police SWAT forces could be seen on the roof of the building and one police helicopter landed near it.
France has been high alert for more attacks since the country’s worst terror attack in decades the massacre Wednesday in Paris at the satirical newspaper Charlie Hebdo that left 12 people dead.
Minutes earlier, a gunman holding at least five hostages in a Paris kosher market had threatened to kill them if French authorities launched an assault on the two brothers, a police official said. The two sets of hostage-takers know each other, said the official, who was not authorised to discuss the rapidly developing situations with the media.
The Paris mayor’s office announced the closure of all shops along Rosiers Street in the city’s famed Marais neighbourhood in the heart of the tourist district. Hours before the Jewish Sabbath, the street is usually crowded with shoppers French Jews and tourists alike. The street is also only a kilometer (a half mile) away from Charlie Hebdo’s offices.
Brothers Cherif Kouachi, 32, and Said Kouachi, 34, grabbed a hostage early Friday and were cornered by police inside a printing house in Dammartin-en-Goele, northeast of Paris.
At least four hostages dead at Kosher store
At least four hostages at a siege of a kosher supermarket in eastern Paris have been killed, a police union source told Reuters.
Earlier, television images showed a group of hostages running out of the store.