Ahmad was in France to attend the 69th FIFA Congress which ended on Wednesday. His passport has been handed to him, meaning he is free to travel, a section of reports said.
The probe by the Central Office for the Fight against Corruption and Financial and Tax Offenses (Oclif) was over a contract that CAF terminated with German equipment manufacturer Puma in favor of Technical Steel.
The French authorities said Ahmad forced CAF to buy sportswear through a French company rather than directly from manufacturers and at inflated prices.
Ahmad is accused of having influenced this decision, standing to be rewarded with up to $830,000. He has denied the allegations.
The world football governing body confirmed the French probe and said it had requested more information. CAF itself has yet to officially comment on the issue.