You should be able to do this fairly easily. Get a Jamma fingerboard and a European RGB SCART cable (I'm assuming here that NTSC 360's will work in RGB mode...), cut the SCART plug off and match up the composite sync, red, green, blue and ground to the fingerboard.
Controllers are going to be another task, I'd take a 360 controller apart and see if the D-pad and buttons work with a common ground. If they do, then it's just a simple matter of wiring those up to the finger board - solder wires to the contact pads and run them to the appropriate pins on the fingerboard. If they *don't* use a common ground, then you'll have to build a custom control panel harness with the wiring scheme of the Xbox controller.
-Ian