Bernard Planche, 52, ran away from a farmhouse where he was being held after his captors fled US and Iraqi troops who were conducting a search of a rural area on the western outskirts of the capital, the US military said on Sunday.
Iraqi security sources had earlier suggested that the hostage, who escaped on Saturday, got away from a car after his kidnappers panicked at a military checkpoint west of the capital.
Planche got out through a window of the farmhouse after his captors suddenly abandoned the farm, Major Jim Crawford told AFP.
"When he realised he was alone and saw US forces in the distance, he escaped through a window and ran down the road," Crawford said.
"He had his hands in the air and, as he approached the US checkpoint, he took his shirt off to show he had no explosives on him."
US and Iraqi forces were searching the area after receiving information on the possible presence of arms caches and of a kidnapping ring in the area.
The former hostage then insisted on staying with US troops for six hours to help them hunt for his former captors.
Crawford declined to say whether anyone was arrested, but he said that caches of weapons were found in the area.
Planche was held in farmhouse on
the western outskirts of Baghdad
Planche was later debriefed by US forces before being handed over on Sunday to the French embassy in Baghdad.
The Frenchman, who was kidnapped from his home on 5 December, apparently suffered a broken nose when his captors seized him.
But after his release, he was smiling and joking with the soldiers.
Diary and radio
"He gave us information. He was able to recall all kinds of details," Crawford said.
He was held in a half-basement with a boarded-up window, but he was allowed to keep a diary and to listen to a radio.
His captors, calling themselves the Battalion of the Lookout for Iraq in a video broadcast by Al-Arabiya television, had threatened to kill him if France did not "end its illegitimate presence in Iraq".
After Planche's disappearance, French embassy officials said they were frustrated that the engineer had not taken greater care for his safety. He lived alone in a large house without guards, and had been warned by the embassy several times, diplomats said.