Police helicopters circled the stadium as Hollande was rushed back to the interior ministry to deal with the situation. The president's office said he had called an emergency cabinet meeting for midnight (2300 GMT) to manage the crisis.
Police confirmed there had been shootings and explosions at the stadium, but not the number of casualties.
In central Paris, shooting erupted in mid-evening outside a Cambodian restaurant in the capital's 10th district and the Bataclan music hall, where bystanders were evacuated as elite police commandos took up position.
Several witnesses told television stations that up to 60 hostages were being held inside the popular concert venue.
"There are lots of people here. I don't know what's happening, a sobbing witness who gave her name only as Anna told BFM TV outside the Bataclan hall. "It's horrible. There's a body over there. It's horrible."