France said Friday it was working to authenticate the recording.
In it, Droukdel said France would have to negotiate personally with Osama bin Laden to secure the release of five French hostages seized in Niger in September. They are thought to be in Mali.
The recording said that, to ensure the hostages' safety, France must "hasten and take your soldiers out of Afghanistan according to a specific timetable that you announce officially”.
In a statement, French Foreign Minister Michelle Alliot-Marie rejected this, adding that "France is doing all in its power for the hostages, wherever they are, to be freed safe and sound".
President Nicolas Sarkozy on Tuesday said he was "especially worried" about the hostages, most of whom work for nuclear giant Areva and its subcontractors, but said threats would not change French policy.