People said armed men got out of a car and began opening fire in the Burkina Faso capital, Ouagadougou, this morning.
The city mayor said this afternoon the incident was a terror attack carried out by "jihadists".
Police said later they had killed four of the gunmen, but a special forces operation was still underway.
France’s embassy confirmed in a statement it was under attack along with a cultural centre and the army headquarters.
In a post on Facebook, it said: "Attack under way at the French Embassy and French Institute. Stay hidden where you are.”
A witness said smaller explosions came from the army headquarters after a first larger blast, masked gunmen had stormed in and security forces were converging on the scene.
Pictures from the scene showed windows blown out by the blasts and cars covered in debris as smoke filled the air.
Police said security units were deployed to the scene and urged people to stay away from that area.
The US Embassy tweeted: “@Usembassyouaga has received reports of gunfire in downtown Ouagadougou.
