Police raided the International Association of Athletics Federations (IAAF) headquarters in Monaco before charging the 82-year-old Diack, who stood down in August when Britain's Sebastian Coe was elected to head the scandal-tainted federation.
Coe asked to be questioned by investigators over the case during the raid on Tuesday, IAAF spokesman Chris Turner told AFP.
The sensational charges were laid ahead of the release this month of a report by a World Anti-Doping Agency (WADA) commission into allegations of widespread substance abuse in Russia, Kenya and among world champions.
Both were released on bail. A former IAAF anti-doping doctor, Gabriel Dolle, was detained for questioning, they added.
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"Emanating from separate ongoing investigations by WADA's independent commission and the IAAF's own independent ethics commission into allegations surrounding its anti-doping rules and regulations, a French police investigation has now commenced," said an IAAF statement.
"The IAAF is fully cooperating with all investigations as it has been from the beginning of the process."
The statement added that "police visited the IAAF HQ offices yesterday to carry out interviews and to access documentation."
But the inquiry could be spread to other cases involving other nationalities, the source added.