Okay, I've downloaded the driver for that CAC reader and had a look. It's a propriety binary with a shell script installer. The readme file gives me the clue that it was compiled for a Debian or Debian-like system. (probably Ubuntu) Most of these companies don't provide 64-bit compiles, so it's most likely a 32-bit binary.
The Installer probably won't work correctly on a Fedora box and I have no idea how to fix that. On an Ubuntu box, you would need to install the 32-bit libraries to get it to work. (this is a hack, the 'correct' way is to compile for 64-bit, but you don't have that option
I'd say that, depending on how regularly you will be using/needing the reader, you will either have to replace Fedora with Ubuntu/Debian to use it, or setup a usb flash drive with 32bit Ubuntu for occasional use.
They don't state anywhere which system it was compiled for, but in my experience, propriety Linux software normally targets Ubuntu even when they say Debian.