Bernard Planche was released on Saturday by his kidnappers near Abu Ghraib prison, west of Baghdad, and was in the care of the US military, the Iraqi police sources said on Sunday.
It appeared the captors were trying to move Planche from one area to another when they encountered a joint US and Iraqi army checkpoint, the sources said.
They bundled Planche out of their car and escaped.
"He is now safe and in the hands of the US military," the Interior Ministry source said.
In Paris, the office of Jacques Chirac, the French president, confirmed the release: "Mr Bernard Planche was freed yesterday in Baghdad. The president is delighted with this happy news.
"The president thanks coalition forces who enabled this release to happen. He has expressed his gratitude to all those
Office of Jacques Chirac,
the French president
"The president thanks coalition forces who enabled this release to happen. He has expressed his gratitude to all those involved."
Planche, 52, was abducted in Baghdad on 5 December from his home in an upmarket Baghdad neighbourhood.
He had been working for a non-governmental organisation at a water treatment plant in the east of the city.
The little-known group issued a video purporting to show him being held captive and threatened to kill him if France did not "end its illegitimate presence in Iraq".
The French government opposed the US-led invasion of Iraq in March 2003.