18 November 2014
Last updated at 08:57 ET
Mr Lazarevic was snatched by the jihadists in November 2011.
A second hostage, Dutchman Sjaak Rijke, appeared in the video alongside him.
The video of the pair, posted by Al-Qaeda in the Islamic Maghreb (AQIM), was unearthed by terrorism monitoring group Site.
It shows Mr Lazarevic in a dark headscarf and thick beard standing in front of a truck with a black jihadist banner behind him.
Speaking in French, he says that his "life is in danger since France intervened in Iraq".
He also urges President Francois Hollande to secure his release.
Family members say Mr Lazarevic was kidnapped while he was scouting possible sites for a cement factory.
He was taken alongside fellow Frenchman Philippe Verdon, who was shot dead by AQIM in March 2012.
Mr Lazarevic is the last remaining French hostage anywhere in the world.
Mr Hollande's office confirmed the video was genuine, saying it offered "proof of life" and that officials were doing everything they could to secure Mr Lazarevic's release.
'Government responsible' In an interview with France's RTL radio, his daughter said she hoped he would be home by Christmas.
She added: "I was very shocked to see him and it's been very trying to see him like that - very thin and weak".
Meanwhile the Dutch government, reacting to the appearance of Sjaak Rijke in the video, said it would not comment out of respect for the 54-year-old's family.
Mr Rijke, who is also shown bearded and standing in front of a black Islamist flag, says in the video that he is speaking on 26 September - though there is nothing else in the clip to confirm this.
"As of today, I hold my government responsible for any harm that comes to me," he adds.
Mr Rijke was also kidnapped in November 2011, while visiting the Malian city of Timbuktu as a tourist.
It is not clear where the two hostages are being held or whether they are being held together.
AQIM took a number of Western hostages before the French military deployed its forces against the group in January 2013.
There were at one point at least 14 French nationals being held by Islamists in West Africa.
by Rashida Adjani and Biodun Iginla, BBC News Website
The
daughter of a French hostage kidnapped by jihadists in Mali has spoken
of her shock after he appeared in a video clip pleading for his release.
Diane Lazarevic told French radio she was worried about the
health of her 50-year-old father, Serge, who she said appeared frail and
thin.Mr Lazarevic was snatched by the jihadists in November 2011.
A second hostage, Dutchman Sjaak Rijke, appeared in the video alongside him.
The video of the pair, posted by Al-Qaeda in the Islamic Maghreb (AQIM), was unearthed by terrorism monitoring group Site.
It shows Mr Lazarevic in a dark headscarf and thick beard standing in front of a truck with a black jihadist banner behind him.
Speaking in French, he says that his "life is in danger since France intervened in Iraq".
He also urges President Francois Hollande to secure his release.
Family members say Mr Lazarevic was kidnapped while he was scouting possible sites for a cement factory.
He was taken alongside fellow Frenchman Philippe Verdon, who was shot dead by AQIM in March 2012.
Mr Lazarevic is the last remaining French hostage anywhere in the world.
Mr Hollande's office confirmed the video was genuine, saying it offered "proof of life" and that officials were doing everything they could to secure Mr Lazarevic's release.
'Government responsible' In an interview with France's RTL radio, his daughter said she hoped he would be home by Christmas.
She added: "I was very shocked to see him and it's been very trying to see him like that - very thin and weak".
Meanwhile the Dutch government, reacting to the appearance of Sjaak Rijke in the video, said it would not comment out of respect for the 54-year-old's family.
Mr Rijke, who is also shown bearded and standing in front of a black Islamist flag, says in the video that he is speaking on 26 September - though there is nothing else in the clip to confirm this.
"As of today, I hold my government responsible for any harm that comes to me," he adds.
Mr Rijke was also kidnapped in November 2011, while visiting the Malian city of Timbuktu as a tourist.
It is not clear where the two hostages are being held or whether they are being held together.
AQIM took a number of Western hostages before the French military deployed its forces against the group in January 2013.
There were at one point at least 14 French nationals being held by Islamists in West Africa.
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Angola Press Mali hostage daughter's 'shock' at jihadist video 4 hrs ago
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News24 N. African militants release video of French, Dutch hostages 6 hrs ago
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International Business Times UK Al-Qaeda Releases New Video Of European Hostages 8 hrs ago
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FOXNews.com French, Dutch hostages in Mali plea for help 13 hrs ago
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Reuters UK French, Dutch hostages held by Qaeda appeal in video 19 hrs ago
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