The other four hostages shown are South African Stephen McGown, Romanian Iulian Ghergut, Swiss missionary Beatrice Stockly and Colombian nun Gloria Cecilia Narvaez Argoti.
No group had previously claimed responsibility for kidnapping Frenchwoman Petronin, who was abducted in late 2016 by armed men in the northern Malian town of Gao, where she ran an organisation for malnourished children.
After a video clip showing Petronin, the narrator said she was hoping the French president would help return her to her family, according to SITE.
The video was released just before President Emmanuel Macron arrived in Mali on Sunday to consolidate Western backing for a regional anti-terrorist force.
In the video, the hostages are separately introduced by a narrator, who says that so far there have been no negotiations for their release.
The first shown is McGown, who was abducted in Timbuktu, northern Mali, in November 2011.
"It's a long time to be away ... Until when do you think this will come to an end? Now we're making a new video, but I don't know what to say. It's all been said in the past. It's all been said in previous videos I've made," McGowan says, according to a transcription by SITE.
Next in the video is Romanian mineworker Ghergut, who says he was captured in Burkina Faso on April 4, 2015.
The women are then shown, including Swiss missionary Stockly, who was kidnapped in Mali in January 2016.
Colombian nun Argoti was seized by armed men in the Mali village of Karangasso close to the Burkina Faso border in February 2017.
At the end of the undated video, while not spelling out any demands the narrator tells the hostages' families "no genuine negotiations have begun" for their release but then adds that negotiations are "still active".
In 2012, Mali's north fell under the control of terrorist groups linked to Al-Qaeda who exploited an ethnic Tuareg-led rebel uprising, though the Islamists were largely ousted by a French-led military operation in January 2013.
Since then, terrorist have continued to mount numerous attacks on civilians and the army, as well as on French and UN forces stationed there.