The members of the group took the prizes for Best Album and Best Single. They are the first to win both the Mercury Music Prize at the Brit Awards and at the NME Awards in the same year.
Singer for the group, Alex Kapranos stated, "When we got together as a group, we wanted to be like the groups that inspired us, like New Order and Oasis."
Along with Franz Ferdinand, groups The Libertines and Razorlight also took awards at the ceremony held in London.
The winners of the awards were selected by the readers of the magazine New Musical Express.