The intervention came yesterday after the Arab Movement of Azawad (MAA) took the northern desert settlement of Anefis from the National Movement for the Liberation of Azawad (MNLA), a Malian and another African military source said.
But the Malian source, a senior member of the war-torn west African nation's army, described the French intervention as "a bit of a mess".
"France and its partners must treat all illegally-armed groups in northern Mali equally. There should not be any favour or preference for the MNLA," he said.
Mali called in French troops in January to halt an Islamist advance on the capital Bamako.
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French and African troops have since pushed the al-Qaeda-linked militants into desert and mountain hideouts, from where they are staging guerrilla attacks.
The criticism comes as France begins winding down its force of nearly 4,500 in Mali to 1,000 troops who will maintain responsibility for military strikes against the Islamists.
"I am a soldier. I leave the political management to the politicians. I'm talking militarily. Let's refuse to support the taking up of arms by illegal groups," the Malian officer added.
It was not immediately clear if there were casualties in the clashes in Anefis, a town of around 5,000 people 120 kilometres southwest of the MNLA-held city of Kidal.
The MNLA initially led the takeover of northern Mali last year in a bid to split the region from the south, where the government in Bamako has long marginalised their community.
Fighting alongside Ansar Dine (Defenders of the Faith) and backed by the Movement for Oneness and Jihad in West Africa, the Tuaregs were then swiftly pushed aside and the alliance collapsed, with many MNLA fighters instead defecting to Islamist rebel groups.