Hollande called Friday night’s the machine-gun assault a “cowardly attack” on La Terrasse, an eatery near Bamako’s racecourse, and promised that France would do all it could to assist the Malian authorities.
Prime Minister Manuel Valls declared himself “horrified” in a tweet and confirmed that one of the victims was “very probably” a French national and in the process of being identified.
A Belgian was also among the two foreigners killed - early reports put the figure at three but it was later revised downwards.
“It’s disastrous to see this cowardly terror strike in numerous places around the world,” commented Belgian Foreign Affairs Minister Didier Reynders.
One of the Malian victims is reported to be a police officer who was passing by.
Nine people were wounded, three of them Swiss, and the UN said that two mine-clearance experts who were working for it were among the injured.
French soldiers stationed in the city arrived quickly at the scene.
The authorities described it as a terrorist attack and said they had arrested two suspects.
They "are in the process of being interrogated", a source told the AFP news agency, and have begun to give "interesting" information.
Witnesses said four men fled the scene, crying "God is great" in Arabic.