A French official in Paris confirmed that an assault against the embassy was under way, as well as against the Burkina Faso army headquarters. "Monitor local media for updates", it said on Twitter.
France's embassy is no longer in danger, an aide to Mr le Drian said.
The French Foreign Ministry said the situation around the embassy in Ouagadougou has now "stabilized".
"Burkinabe security forces are mobilised against the attackers with the support of security forces at our embassy", said French minister for foreign affairs Jean-Yves Le Drian in a statement.
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. The defence minister said three assailants were killed at the army headquarters.
The government said earlier the capital Ouagadougou was being assaulted by suspected Islamic extremists as explosions and gunfire erupted around the city.
Today's incident defies known patterns of Salafi jihadists in the country, further fueling speculations around its motives.
Men escape from Burkina Faso's army headquarters during an attack in the capital Ougadougou, Burkina Faso March 2, 2018.
French President Emmanuel Macron telephoned his Burkinabe counterpart Roch Marc Christian Kabore to express solidarity and send his condolences to the families and victims of the slain security force members, his office said. Barricades were erected to keep people from that area and from the French Embassy and the prime minister's office in the eastern part of the city center where gunfire and smoke were reported.
The French embassy in Ouagadougou writes on its Facebook page "there is no certainty at the moment" about the places that where targeted.
Witnesses said five armed men got out of a auto and opened fire on passersby before heading towards the embassy in the centre of the city.
Plumes of black smoke could be seen above the army offices in western Ouagadougou where police and gendarmerie responded.
France, the former colonial power in the Sahel region, has deployed 4,000 troops and is supporting a five-country joint force gathering Burkina Faso, Chad, Mali, Mauritania and Niger. They also set fire to the truck, the witnesses added.
The neighborhood also houses other embassies, the prime minister's office and United Nations offices.
On August 13 previous year, two assailants opened fire on a restaurant on Ouagadougou's main avenue, killing 19 people and wounding 21.