Brins,

The simple answer is that some the components will fit both, some won't, and some might.

More specifically, the stem and the seatpost will not. The LeTour will use the small .833 Schwinn sized stem and the Paramount the more standard size (although at this moment I forget that size). You've already noted the size of your seatpost. A Paramount will most likely use a 27.2 (but some use a 27.0).

Brake calipers, BB, and wheels might work. If you have 27" wheels on the LeTour, they will work on some Paramounts, but there are others that ran the 700c size. Brake calipers depend on their reach and the distance that needs to be covered. My limited experience is that every rear brake bridge and front fork gap is different on each model of frames. BB sizes, IMO, are weird, and the only way to fit them is through trail and error. I'd love to learn a better way.

Pedals, crankset, and derailleurs should be universally exchangable. I've hung a Campy RD, FD, and a crankset on a Schwinn Continental with no problems. If I can do that, you can certainly build your LeTour with such components and then move them to a Paramount with no problems.

Best of luck on your projects! Post a picture of your bike.