This may seem like a stupid question but I just want to clarify what Parisian hotels consider a bath & shower. The price is usually cheaper when you get a room with shower so I am assuming it is a shower stall only (except for toilet & sink). A bath would actually have a bathtub and a shower head (sometimes portable). Is this correct. I would never use the bath so what would be the advantage of paying more for it?

Yes. You're correct in your assumptions except not always there is a standing showerhead. It may be a handheld shower. Rooms with tubs cost more as they are usually larger than rooms with shower only.

And sometimes "bath" also means only a bathtub w/o a showerhead.

yeah, this isn't some general thing about Parisian hotels, though, just the one you are looking at. Many of them have a shower head in a tub and not only a stall, so then the price of a room probably won't differ for that reason. But you can assume if it's cheaper for the shower, it's a smaller room in some way, even if only the bathroom. Some hotels actually have rooms with tubs that tend to be the superior rooms over shower-only, and the entire room is a bit larger. So don't assume it's just the bathtub difference.

Thanks for the info. Better to be safe than sorry.