Two gunmen ran out of the nightclub and jumped into a car driven by an accomplice, said witness Hamadou Dolo. They ran into a police patrol about a block away and fired on the police car, killing its driver, a civilian in the street and a private security guard outside a house, said Dolo.
La Terrasse is in Bamako's Hippodrome neighborhood where many expatriates live and the nightclub is popular on a Friday night for salsa dancing.
French President Francois Hollande's office said five people had been killed and others injured and that security had immediately been tightened around French facilities. A statement from his office said the French embassy has set up a crisis cell to help expatriates in Bamako.
Hollande said that he will speak with Mali's President Ibrahim Boubacar Keita to show his support, much as the Malian leader visited Paris to show his support in the wake of the Charlie Hebdo attacks in January.
France immediately opened a judicial inquiry, a standard procedure when a citizen is killed which allows French officials to carry out a parallel investigation, according to a judicial official in Paris who spoke on condition of anonymity because he is not authorized to speak on the matter.
French forces led a military operation in early 2013 that largely expelled al-Qaida-linked extremists from a vast area they had controlled in northeastern Mali. The military operation in that region continues, and sporadic combat and clashes take place there. Violence has been rare in Bamako despite the continued upheaval in the north.