Al-Jazeera broadcast the tape purportedly posted by al-Qaida, France 24 reported.
Bin Laden warned France would pay a "high price" and the hostages' lives depend on its troops getting out of "Muslim lands."
"We repeat the same message to you: The release of your prisoners in the hands of our brothers is linked to the withdrawal of your soldiers from our country," bin Laden said. "The refusal of your president to withdraw from Afghanistan is the result of his obedience to America and this refusal is a green light to kill your prisoners."
France has not confirmed the tape's authenticity.
A bin Laden message broadcast on al-Jazeera in October said the September kidnapping of seven foreigners, five of them French citizens, in Niger was in retaliation for French "tyranny ... against our Muslim nation."
Al-Qaida in the Islamic Maghreb has claimed responsibility and says France must talk directly to bin Laden to free them.
Two French journalists also have been held captive in Afghanistan since December 2009.