"The exit of your hostages out of the hands of our brothers depends on the exit of your troops from Afghanistan," bin Laden said in the message broadcast by Al-Jazeera.
Extremist groups associated with al Qaeda are holding at least seven French hostages, including five in the Sahara Desert and two in Afghanistan.
France has about 3,850 troops in Afghanistan as part of the NATO mission fighting the Taliban. French forces are deployed mainly in the Kapisa and Surobi districts north and east of Kabul, the Afghan capital.
French President Nicolas Sarkozy has said his nation remains undaunted in its role to help stabilize Afghanistan.
French Foreign Ministry spokesman Bernard Valero said Bin Laden's message was still being authenticated. "We are determined to continue our efforts on behalf of the Afghan people, with our allies," Valero said.
France, Germany and Britain have been on a heightened state of alert since last September amid fears that teams of gunmen were planning to attack densely populated areas like tourist sites or transportation systems, reports CBS News' Charles D'Agata.
Bin Laden reminded the French people of Sarkozy's refusal in November to withdraw French troops from Afghanistan and to negotiate with al Qaeda over the hostages.
"Your president's rejection is a result of being a hireling to America and is a green light to kill the hostages. ... His stand will cost you a high price on different aspects inside or outside France," he said.
The al Qaeda leader questioned why the French would consider the resistance against Nazi German troops occupying their nation in World War II to be heroic while the fight against French and other foreign troops in Afghanistan is labeled terrorism.
"Why do you judge in a double standard?" he said.
Bin Laden also challenged whether the state of France's economy would allow it to wage a successful fight against al Qaeda.
"The size of your debts and the weakness of your budget will not allow you to open a new front," he said.
Al Qaeda has often sent audio messages to Al-Jazeera for broadcast. Bin Laden's last tape, sent Oct. 27, also warned France over its Afghanistan presence and measures banning Muslim garb.