The state broadcaster RTB showed video of soldiers closing around one of the buildings involved, with gunshots echoing, a helicopter swooping low overhead and a car ablaze nearby.
In 2016 and again last year, jihadists attacked civilian sites that were popular with Westerners — cafes and a hotel — killing a total of 49 people.
Paul Kaolaga, a terrorism analyst with the Strategic Network on Security in the Sahel, said the military, supported by French special forces, had reasserted control at both attack scenes.
In recent years, Al Qaeda in the Islamic Maghreb has pushed south from its base in Algeria, into Mali, and then to Burkina Faso. In aiding the fight against terrorist groups, Mr. Kaolaga said, Burkina Faso has become one of their targets.
Aurélia Laget, a spokeswoman for the French Institute in Ouagadougou, which is near the embassy, said that workers there had taken shelter and that sounds of fighting had gone on for more than an hour. “We heard gunfire for sure, and explosions, I think,” she said.
Some witnesses said the gunmen at the embassy set fire to their vehicle when they arrived, which could have caused an explosion.
President Emmanuel Macron of France called President Roch Marc Christian Kaboré of Burkina Faso and condemned the attack in “the strongest terms,” Mr. Macron’s office said in a statement.
France leads a 5,000-member multinational force — including troops from Burkina Faso, Mali, Niger, Chad and Mauritania — that is trying to combat terrorism in the region.
The State Department urged Americans on Friday to reconsider travel to the country.
“Terrorist groups continue plotting attacks in Burkina Faso,” it said in a travel advisory. “Terrorists may conduct attacks anywhere with little or no warning. Targets could include hotels, restaurants, police stations, customs offices, military posts, and schools.”
Blaise Compaoré, the longtime president of Burkina Faso, a former French colony once known as Upper Volta, was ousted in a popular uprising in late 2014; a coup was mounted the following year but ultimately failed. Mr. Kaboré took office at the end of 2015.
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