i am an exchange student but in my school they use the term salle de musculation. I think this term is easily understood to be the gym.

You will find different terms:

salle de fitness

salle de gym

salle de sport

Salle de remise en forme can be found, but as you suggested, it would be used specifically for programs aimed at people that are out of shape and want to become fit again, so that does not really fit the fitness rooms you can find in hotels (or, I can imagine a hotel may use this term if it sells such a program as part of a package).

Salle de musculation is not wrong either, but is more specific. Such a room will offer primarily equipment used for bodybuilding (eg for weight lifting), and may not have things like running machines or stationary bicycles. You may find salles de musculation in town or in sport centres, but it does not match the typical fitness room you will find in hotels.