Yes, it's absolutely possible to study Drama and a foreign language at university. Many universities offer combined honours degrees, allowing you to study two subjects simultaneously. You might find a specific "Drama and Modern Languages" program, or you could combine Drama with a specific foreign language (e.g., Drama and French, Drama and Spanish) as a joint honours or combined honours degree. Alternatively, you could study Drama as your primary subject and take foreign language courses as electives.
The availability of specific combinations will depend on the university and its course offerings. It's best to research universities directly and look at their program brochures or websites to see what options are available.