Originally Posted by AEO
the tapering for a sugino triple should be JIS, which is what shimano uses. Peugeot used 'french threaded BB' so yes, you will need to buy a new BB to use it on your rock hopper.
typically, you'd want a 113mm BB axle length for a sugino triple. It might have to be longer depending on how bowed your chainstays are.
Just to clarify something here, there are two different factors at play, one is the threading of the bottom bracket cups, and the other is the taper of the spindle itself. The peugot likely has french threaded bottom bracket cups that will not fit into your frame. The spindle also likely has a different taper (ISO vs JIS). Long story short, it still won't work, but for many different reasons.
The Barcons can shift just about anything, so as long as your crank clears the frame you're good to go. It's always worth just giving it a try using the parts on hand. Both the Shimano crankset on the rockhopper and the Sugino on the Peugot should use JIS taper, and you have nothing to loose by throwing the triple on just to see if it fits.
If it bottoms out and the inner chainring rubs against the frame, then you need a new bottom bracket (Shimano UN-52, it's like $25) Otherwise you're good to go.
With friction Barcons, you don't really need to worry about derailer compatibility.