I don’t believe that Sheiks go to France for medical care. With the hospitals in Riyadh, Dubai, even throughout Kuwait - those hospitals make sci-fi seem real, and they aren’t for anyone but arab elites. Such as Sheiks.
You are correct about medical tourism. It is very big. And, increasingly, it’s not just for the uber rich. Jordan and Singapore also generate big money through medical tourism.
They end up going to places like the Cleveland Clinic.Especially for heart surgery.