French army spokesman Col Thierry Burkhard confirmed that "French elements were deployed overnight in Kidal".
French forces now control Kidal airport after a number of aircraft, including helicopters, landed there overnight.
It is thought the mountainous areas around Kidal provide perfect hiding places for the militants.
The French arrival at Kidal airport came only 24 hours after securing Timbuktu with Malian forces.
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He later said that Mujao had detonated a car bomb near a military base in Kidal.
Kidal remains the only major town not under the control of French and Malian forces.
When French troops seized Kidal's airport a month ago, the MNLA took control of the town itself.
Once Kidal is taken, the first phase of the French operation will be over, our correspondent says.
Major cities such as Gao, Kidal and Timbuktu fell and a strict form of Islamic law was imposed.
About 229, 000 Malians have been displaced -- mainly from Kidal, Timbuktu, and Gao, according to the United Nations.
French forces are continuing to carry out air strikes in mountains north of Kidal where Islamists have taken refuge.
In March and April they had seized the key towns in Mali's north - Kidal, Timbuktu, Gao and Niafounke.
Their presence in Kidal explains why government troops have not yet been sent to the town, our correspondent adds.
BBC: French troops in Mali take Kidal, last Islamist holdout
An MNLA spokesman told the BBC its fighters had entered Kidal on Saturday and found no Islamist militants there.
BBC: French troops in Mali take Kidal, last Islamist holdout
Earlier, the French military said some 1, 800 soldiers from Chad had entered Kidal.
Earlier this month, some 1, 800 Chadian soldiers began patrolling the city of Kidal.
The French-led forces faced little resistance during the initial offensive, when they recaptured major towns of Gao, Kidal and Timbuktu.
They are attempting to secure the north-eastern city of Kidal, the militants' last stronghold, having captured the airport on Wednesday.
Some 1, 000 Chadian troops began moving out of Kidal toward the wild Ifhogas mountains further north and the Algerian border.
When French troops moved into Kidal, a distant and largely Tuareg town this week, they took the town without Malian troops.
The latest French strikes had been targeting rebel command centres, training camps and depots north of Kidal, an army spokesman said.
Kidal, Gao and Timbuktu experienced days of looting, abductions and chaos after they were occupied by armed groups late last week.
Since the intervention began, major cities including Gao, Kidal and Timbuktu have been recaptured but fighting is still continuing in desert mountains.
Our correspondent says French forces who entered Kidal found members of the secular National Movement for the Liberation of Azawad (MNLA) there.
BBC: French troops in Mali take Kidal, last Islamist holdout
According to the statement, the faction is headed by Alghabass Ag Intalla, an important Ansar Dine leader and influential figure in Kidal.
The Islamists were reported to be fleeing Timbuktu to the city of Kidal, more than 500 kilometers (310 miles) to the northeast.
Once Timbuktu is secured, the French-led troops are expected to focus on the last rebel stronghold, Kidal, near the border with Algeria.
The Islamists were reported to be fleeing Timbuktu to the city of Kidal, more than 500 kilometers (300 miles) to the northeast.
They are then expected to focus on the last rebel stronghold, Kidal.
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In another northern city, Kidal, residents were fleeing their homes, Amnesty reported.
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