As far as I know the only part FreeCAD that can use multiple CPU cores (indirectly) is FEM workbench when running CalculiX.
It's hard to define minimum spec, because it heavily depends what you want to do. I'm quite sure that if they have other CAD software running right now the hardware will be good enough to run FreeCAD.
I use on-board intel HD4000 graphics card and it works fine, but I don't do anything very complicated.
P.S. Has anyone tried to compile and run FreeCAD on raspberry pi?
Edit: I just found info that FreeCAD runs on raspberry PI (raspbian, wheezy and jessie), so probably it can run on just about anything