BBC News reports: The French arrival at Kidal came only 24 hours after securing Timbuktu with Malian forces.
The troops had to secure the streets after hundreds of people looted shops they said had belonged to militant sympathisers.
The retreating Islamist militants were also accused of destroying ancient manuscripts held in the city.
However on Wednesday, Shamil Jeppie, the Timbuktu Manuscripts Project director at the University of Cape Town, said that more than 90% of the 300,000 manuscripts said to be in the region were safe.
Kidal, 1,500km (930 miles) north-east of the capital Bamako, was until recently under the control of the Ansar Dine Islamist group, which has strong ties to al-Qaeda in the Islamic Maghreb (AQIM).
The Islamist militants had taken advantage of a military coup in March last year to impose Sharia in a number of cities in the north.
However, the Islamic Movement of Azawad (IMA), which recently split from Ansar Dine, says it is now in charge in Kidal.
The IMA has said it rejects “extremism and terrorism” and wants a peaceful solution.
An IMA spokesman confirmed the French arrival in Kidal and said that its leader was in talks with them.
However, another rebel group, the secular National Movement for the Liberation of Azawad (MNLA), is also influential in the area. It is ethnically driven, fighting mostly for the rights of Mali’s minority Tuareg community.
An MNLA spokesman told the BBC its fighters had entered Kidal on Saturday and found no Islamist militants there.
The MNLA has also said it is prepared to work with the French “to eradicate terrorist groups” in the north but that it would not allow the return of the Malian army, which it accused of “crimes against the civilian population”.