Would a more accurate translation not be Sports hall. Other latin languages have similar words m=which mean hall - Salla in Italian, sala in spanish for instance
"Sports hall" encapsulates the meaning much better, but if you tell an English person you're going to a "sports hall", they're going to be a bit confused as to what exactly goes on behind closed doors in this "Hall of Sports". <:-O
Just saying "gym" doesn't do it justice though, since it's not just an exercise place (with weights and machines etc) but also usually has climbing racks, handball and basketball courts etc. built-in to the building.