Romeo Langlois fell into rebels hands on April 28 while accompanying troops on a cocaine lab destruction mission in the jungles of southern Colombia. Rebels attacked, killing four security force members. Langlois was wounded in the arm.
Colombia's defense minister says a witness saw Langlois shed the helmet and body armor the military had given him and flee toward the rebels. The military unit had destroyed other labs in the area and was ambushed after arriving by helicopter.
Langlois, 35, was on assignment for France24 television. He has been reporting from Colombia for more than a decade and has also contributed to the French daily Le Figaro.
Reached in Mexico, Cordoba said she would return to Colombia immediately. A friend of Venezuelan President Hugo Chavez, Cordoba has brokered rebel hostage releases since 2008.
The rebels, known by their Spanish initials FARC, took up arms in 1964 and announced in February that they were halting ransom kidnappings. Last month, they released 10 police and soldiers they called their last "political prisoners."