Francois Hollande has called the Paris attacks "a nightmare".
Dozens of people were killed in a series of attacks in the French capital. Elite police units launched an assault on a theatre in the city where a concert was taking place until an attack. The police killed two gunmen.
In a televised address, Mr Hollande said the nation would stand firm and united against the terrorists.
"It's a horror," Mr Hollande said, adding that the military is being deployed around the capital.
The residents of Paris have been asked to stay home and several Metro lines have been closed.
In the 10th arrondissement - not far from the offices of magazine publisher Charlie Hebdo - police say 11 people were killed near the restaurant.
Witnesses have described seeing bodies lying in the streets. According to local media reports, the gunmen have not been caught.
Elsewhere in the capital, several explosions were heard at the Stade de France, where the national football team was playing Germany.
French football officials say one of the explosions was at an entrance to the stadium.
Mr Hollande was inside the stadium at the time, but was rushed to the Interior Ministry to deal with the unfolding crisis.
An Associated Press reporter who was also at the stadium has recounted hearing two explosions that were loud enough to penetrate the sound of cheering fans.
Those at the stadium can be seen rushing onto the pitch after hearing the explosions.
US President Barack Obama has described the attacks as an "outrageous attempt to terrorise civilians" and has promised to do everything he can to bring those responsible to justice.
"Those who think that they can terrorise the people of France or the values that they stand for are wrong."
British Prime Minister David Cameron said he is "shocked" by violence.
"Our thoughts and prayers are with the French people. We will do whatever we can to help," he said on Twitter.
France has been on edge since deadly attacks by Islamic extremists in January on satirical newspaper Charlie Hebdo and a kosher grocery that left 20 dead, including the three attackers.
- The Department of Foreign Affairs says anyone concerned about Irish nationals caught up in the attacks should call 00 3531 408 2000.
- Anyone concerned about British nationals caught up in the attacks should call 004420 70081500.
In New York, an extra security team has been deployed to the French embassy "out of an abundance of caution" in the wake of the attacks.
Image: Mary Altaffer / AP/Press Association Images
They have stated that there has been "no indication that the attack has any nexus to New York City".