French Defence Minister Jean-Yves Le Drian says his country's military intervention in Mali is aimed at restoring government control over the entire country.
France has sent in 2,000 troops to help Malian forces fight Islamist militants who now control the northern half of the country.
Mr Le Drian said French air-raids are hitting targets in the regions of Gao and Timbuktu, but acknowledged its forces had not yet secured control of the town of Diabaly, north of the capital Bamako.
However, he added that "everything points to a favourable evolution of the situation in Diabaly in the coming hours".
Mr Le Drian also said during his interview that seven French citizens who have been taken hostage in Niger and Mali in recent years "are alive", and there have been "contacts with hostage-takers".
There had been concerns for their fate following France's decision to send troops into Mali earlier this month.