A statement released from Hollande's office, said he telephoned Keita to congratulate him on his victory and assured him that "France will stand by Mali".
Hollande hailed Mali's presidential election as a victory for democracy and vowed France would stand by the west African country, said the statement.
"What has happened in Mali since France sent troops to Mali until the election of a new Malian president, is a success for peace and democracy," Hollandesaid. "But now everything must be done to ensure the success of the end of the transition, dialogue and Mali's development."
Hollande is likely to travel to Mali to attend the inauguration of president-elect Keita.
For several decades after independence from France in 1960, West African country of Mali, one of the poorest in the world, suffered droughts, rebellions, a coup and 23 years of military dictatorship until democratic elections in 1992.
The country saw a flourishing democracy and relative social stability in the 1990s but the stability was interrupted in early 2012 when the state control over the north of the country decreased with unrest followed by a military coup that later caused a French military intervention.
France sent troops to Mali in January 2013 to push Islamist rebels, who threatened to advance south, out from the north and it began withdrawing some of its troops from the country in April handing over its military role to a UN-mandated African force.
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