The ruling secretariat of the Revolutionary Armed Forces of Colombia, or FARC, did not say if or when the insurgency plans to release Romeo Langlois.
It noted, in a communique published online that Langlois "was dressed in military clothing of the regular army" on April 28 when security forces he was accompanying on a cocaine lab-destruction mission were attacked by the FARC.
Accompanying the military on such missions serves the government's propaganda purposes, said the statement, which was dated May 3.
"We think the minimum that can be expected for the recuperation of (Langlois') full mobility is the opening of a national and international debate over the freedom to inform," it continued. "Journalists that Colombia's armed forces take with it on military operations don't adhere to the impartial purpose of informing about reality."
Colombia's defense minister has said that during the combat Langlois removed the helmet and flak jacket that the army had provided and identified himself as a civilian.
The statement, published by the sympathetic Sweden-based ANNCOL news agency, began with the FARC leadership announcing "the detention in the quality of prisoner of war the French journalist Romeo Langlois by units of the FARC's 15th Front.".
It warned Colombia's military not to try to rescue Langlois, referring to previous instances when it has killed "prisoners" during perceived government rescue attempts.
Earlier on Sunday, in a video released by independent journalist Karl Penhaul, a man who identifies himself as a rebel squadron leader said Langlois was lightly wounded in an arm but was out of danger.
It shows armed men and women in fatigues in a jungle area.
The rebel says they are from the 15th Front of the Revolutionary Armed Forces of Colombia and that it captured Langlois in a 7-hour firefight.
He said that now that the rebels know Langlois is a journalist "we hope to quickly overcome this impasse."
Langlois, 35, was on assignment for France24 television and has also done work for the newspaper Le Figaro. He has been working in Colombia for more than a decade.
Penhaul said the video, released on YouTube, was recorded Saturday.
In its statement, the FARC's secretariat complained about its own Web site being "attacked and permanently blocked."
Indeed, the FARC periodically changes Web addresses, whether because of cyberattacks or removals ordered by foreign governments where they are hosted.
The FARC took up arms in 1964 and is estimated to have about 8,000 fighters.
It has in recent years suffered a series of major setbacks, including the killing last year of its top commander, Alfonso Cano, and has been urging the government to enter into a peace dialogue.
President Juan Manuel Santos says the FARC has not met his conditions for talks, and insists it must honor its February pledge to halt ransom kidnappings.
The rebels released last month what they said were their last "political prisoners," 10 soldiers and police they had held for as much as 14 years.
Associated Press writer Frank Bajak reported from Lima, Peru