In Mali street battles are said to have been taking place between French special forces and Islamist militants in the town of Diabali, which fell into rebel hands on Monday.
Reports say French troop reinforcements have been arriving in the zone where jihadist groups are active.
French and Malian soldiers have been heading north from Bamako, the African country’s capital, as the ground operation gets underway.
On Tuesday hundreds of troops headed north from Niono. Diabali, 50 kilometres away, was bombarded several times by the French air force.
But witnesses say militants are still there.
“We’re in a better position than last week but the combat continues and it will be long, let’s be honest, the goal is to make sure that Mali regains all of its territory’s sovereignty,” said the French Defence Minister Jean-Yves Le Drian.
In Bamako there is a sense of relief at the French intervention.
“I am happy, very happy about the arrival of the French, for the freedom of the Malian people. There you are. We want the unity of our country and a Republican state and throw out once and for all the terrorists and narco-traffickers,” said resident Oumar Camara.
President Hollande has said the aim is to “destroy the terrorists”.
The number of French troops in the country is set to treble, before a West African force becomes operational.
Army chiefs from the West African force are meeting in Bamako to fine-tune the operation, being launched under a UN mandate.