In the video, posted online yesterday, the hostage identifies himself as 63-year-old Francis Collomp, an engineer with the French firm Vergnet, who was "kidnapped in Rimi in Katsina state on 19 December 2012 till today, 25 September 2013."
The hostage appears wearing a white t-shirt, with an unidentified person holding a weapon in the background.
If authentic, it would be the first video of Collomp to emerge since his abduction.
The abductee's brother, Denis Collomp, told AFP of his relief at seeing the images, while still fearing for his safety.
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But he added: "Ansaru have never released a single hostage, so it's still very worrying," recalling that his brother had undergone a triple heart bypass years ago.
Parts of the short video statement are not clear, but Francis Collomp can be heard calling for "negotiations" for his "safe release."
In the latter half of the three-minute video, the camera focuses on an Arabic statement that addresses "the government(s) of France and Nigeria," according to the translation provided by SITE.
While there is no direct threat of further attacks, or on Collomp's life, the statement vows to treat "treachery and treason" by the French or Nigerian governments with "reciprocity."
Ansaru is considered by some to be a breakaway faction of Boko Haram, Nigeria's more prominent Islamist group which has waged a deadly insurgency since 2009.
The links between the two organisations remain in question, but some analysts have said that Ansaru might have emerged from a faction within Boko Haram that sought to specifically target foreign interests.
Ansaru has been blamed for the 2011 kidnapping of a Briton and an Italian national in northern Nigeria. Both hostages were killed in March of last year.