French troop reinforcements being sent to Kidal have been delayed by a sandstorm near the north Malian town.
But the French defence minister denied that forces were stuck at the airport, and military officials are quoted as saying that soldiers have since been patrolling the streets.
They reportedly met no resistance. Kidal was the last urban bastion held by al-Qaeda-linked rebels.
The capture comes days after French and Malian forces took control of Gao and Timbuktu.
“The president had wanted us firstly to halt the jihadists’ progress towards the south. That was done immediately,” the French Defence Minister Jean-Yves Le Drian told France Inter radio. “Secondly, he explained that we needed to accompany the Malian – and, when they’re established, the African forces – in recovering Mali’s territorial autonomy and integrity. It’s underway, a lot faster than some imagined.”
France is planning to hand over its mission to a larger African force. The small town of Ansongo near Gao welcomed troops from Niger as they passed through.
The United Nations Security Council is to consider deploying UN troops – a development the French defence minister has described as “extremely positive”.