In a written appeal, Philippe Douste-Blazy said that nothing justified the captivity of the French engineer Bernard Planche, who was kidnapped on 5 December.
Douste-Blazy also reminded the kidnappers that France has no troops in Iraq.
On 28 December, the Arabic television station Al-Arabiya aired a video from an Iraqi militant group claiming responsibility for Planche's kidnapping.
The group has demanded that France end "its illegitimate presence in Iraq" or they would execute their hostage.
Paris was one of the strongest opponents to the U.S.-led invasion of Iraq in March 2003.