Officials identified him as Bernard Planche, who worked at the Rusafa water treatment plant in eastern Baghdad. It was the third kidnapping of Westerners in Iraq in 10 days.
Planche was kidnapped on Monday by seven armed men in two cars as he prepared to leave his home in the west Baghdad district of Mansur, police quoted witnesses as saying. Small pools of blood were left outside the gates of his house.
One neighbour, who declined to be named, said: "The whole neighbourhood watched and no one did anything to help him. The Frenchman had his hands in the air and was screaming."
In Paris, Jean-Baptiste Mattei, the French Foreign Ministry spokesman, declined to confirm the kidnapping.
"We are checking with our embassy in Baghdad and hope to have more details in the coming hours," Mattei said.
A French embassy official in Baghdad said he was trying to get information.
Planche's abduction follows the abduction of Susanne Osthoff, a German archaeologist and aid worker, on 25 November and that of four Christian peace activists - two from Canada and one each from Britain and the United States - the following day.
German aid worker Osthoff has
also been taken hostage
The recent spate of kidnappings follows a lull in abductions of Westerners in recent months, as most foreigners cut back on all but essential travel around Baghdad.
The French government, which opposed the US-led invasion in March 2003, has taken strong measures to dissuade its citizens from venturing into Iraq after two kidnappings involving French journalists in 2004 and earlier this year.
Iraqi officials went so far as to expel a French freelance reporter from Iraq in June citing threats to her security, a decision the journalist said was taken at the French government's request. France, however, said that it was a sovereign decision made by Iraq.
Previous French hostages were freed amid speculation of ransom payments, though the French government denied that too.