Hollande called on the United Nations to address lingering insecurity in Mali, divided when Islamic and foreign rebels claimed autonomy for the northern section of the country.
He said the French government was prepared to support any action at the Security Council that would bring an end to a crisis simmering since March.
"Mali must regain control of its territory and terrorists must be driven from this region," he said during his address.
The central Malian government in Bamako agreed to host 3,000 members of a military unit backed by the Economic Community of West African this week.
The International Crisis Group had warned a coup was possible given the protracted conflict in Mali, saying force may be necessary to "neutralize" rebel groups that pose a threat to the country's territorial integrity.
In a report published early this week, Human Rights Watch said rebel groups in northern Mali, including al-Qaida affiliates, are suspected of recruiting child soldiers, summary executions and razing internationally protected sites in the region.
Mali gained independence from France in 1960.