As folks are indicating, BB shell width is the first thing to check. The (careful) cup checks are also a good idea.

If you measure the I.D. of the BB shell threads, British threads should be about 33.8 mm or so, whereas Italian threads should be more like 34.8 mm. I.D.

Remember also that sometimes stripped non-Italian threads were reamed out / re-tapped to Italian as a repair, though, so a 68 mm wide Italian-thread BB can occur on an old frame. I think there were also some Italian marques (certain very old Cinellis, for example, iirc? Not to mention their 74 mm ones...) that had 68 mm shells that were Italian threading.

Edit: French/Swiss BB shell threads should be about .2 mm larger than BSC, or approx. 35 mm I.D. Unfortunately, that is very close to BSC (no surprise), and the I.D.s can vary a bit, so that's not a great way to distinguish French/Swiss from BSC on used frames.