“It is essential that hostilities cease and that inclusive talks begin,” declared Romain Nadal of the French foreign ministry.
Tuareg insurgents wrested control of the town, a stronghold of their separatist movement, on Wednesday night.
The fresh fighting ended an uneasy calm which had prevailed since the MNLA
took 32 civil servants hostage during a May 17 battle that left eight Malian soldiers and 28 rebels dead.
Military operations against militant groups in Mali are complicated by the fact that fighters move between separatist and Islamist causes, while even the Malian army employs thousands of former Tuareg rebels.
President Ibrahim Boubacar Keita called for an "immediate ceasefire" in the fighting in Kidal that had left "several wounded and caused the loss of human life", the government said in a statement.
"The Malian government forces no longer hold any positions in the city," the Minusma (United Nations peacekeeping force) source said.
In Bamako, several organisations have announced demonstrations against the "occupation of Kidal", some accusing France and the UN of apathy in the face of Tuareg aggression.
A French school in Bamako did not open on Thursday, according to a message
from the French consular authorities in Mali.