France established a military presence in the Sahel nation in January 2013 to combat Islamists including the group behind the video, al-Qaeda in the Maghreb (AQIM), which had overrun key northern cities.
The images released late Friday show the public execution of two men, named as Mohamed Ould Beih and El-Hussein Ould Badi, who were respectively accused of being paid to recruit informants and of showing French troops jihadists' weapon stashes.
Badi was also accused of collaborating with Mauritania to provide it with intelligence about jihadist fighters in Libya.
The clip entitled "Traitors 2" was released by AQIM's media arm Andalus Media, lending it significant credibility.
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It appears to be a sequel to a December 2015 video named "Traitors" in which two Malians and a Mauritanian were killed for similar reasons, also before an audience.
The men in the latest video are identified as being from Timbuktu in northern Mali, but the site of the killings is not identified.
The jihadist group Ansar Dine, which also has ties to Al-Qaeda, claimed that attack on social media.
Jihadists have been driven back from Mali's main cities due to French operations and the presence of a UN mission, but vast swathes of the country remain out of the control of Malian and foreign forces.