The militant Islamist fighters left the town, near the Algerian border, and are now believed to be hiding in the surrounding mountains.
Kidal was captured days after French and Malian forces retook the provincial capitals Gao and Timbuktu.
Haminy Maiga, a Kidal official, said the troops who arrived aboard four planes had met no resistance.
“The French arrived aboard four planes,” said, Mr Maiga, who heads the regional assembly.
“They took the airport and then entered the town, and there was no combat. The French are patrolling the town and two helicopters are patrolling overhead.”
Earlier, French Defence Minister Jean-Yves Le Drian said a sandstorm had delayed the troops from leaving the airport and entering the town.