The 2001 attacks killed thousands of Americans, and had profound consequences across the globe.
Interior Minister Bruno Retailleau accused him of authoring social media posts which "glorified terrorism".
Mitchell Brewing Co, of Lincolnshire, had to unplug phones and close its website because of demand.
After more than 20 years on the run, al-Qaeda boss Ayman al-Zawahiri died in a US drone strike on Sunday.
Where is al-Qaeda 20 years after the 9/11 attacks - and could it re-emerge as a terror threat?