"This political process now has to advance concretely," French foreign ministry spokesman Philippe Lalliot said Wednesday.
He called for talks with the legitimate representatives of the northern peoples and "non-terrorist armed groups" that recognise the integrity of Mali.
"Only a north-south dialogue will prepare the ground for the Malian state to return to the north of the country," he said.
The United States also called for Malians to refrain from revenge attacks on Tuaregs or other ethnic minorities.
French troops arrived at Kidal airport in the early hours of Wednesday, just days after the capture of Gao and Timbuktu and after a lightning push north, which Paris hopes now to wind down with a handover to African forces.
French Defence Minister Jean-Yves Le Drian said Wednesday the troops at Kidal had been unable to leave the airport there because of a sandstorm.
But a spokesman for the newly formed Islamic Movement of Azawad (MIA), which on Monday announced it had taken control of the town, said its leader was speaking to the French there.
The MIA says it has split from the home-grown Islamist group Ansar Dine ("Defenders of the Faith"), that it rejects "extremism and terrorism" and wants to find a peaceful solution to Mali's crisis.
On Wednesday, the group appealed to the international community to prevent the deployment of Malian and West African troops in the Kidal region before a political solution had been found.
Kidal lies 1,500 kilometres (930 miles) northeast of the capital Bamako and until recently was controlled by the Islamists of Ansar Dine.
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Ansar Dine and two other Islamist groups took advantage of the chaos following a military coup in Bamako last March to seize the north, imposing a brutal form of Islamic law.
Offenders suffered whippings, amputations and in some cases were executed while Islamists also destroyed sacred shrines they considered idolatrous in the ancient city of Timbuktu.
France swept to Mali's aid on January 11 after an Islamist advance south towards Bamako sparked fears the whole country could become a haven for terrorists. They now have 3,500 troops on the ground.