Generally, knowing how to program is more important than any specific language. Once you get the hang of it, one can learn (the core of) a new language is a week or two. Sure, learning the core libraries and other APIs takes longer, but unless you know exactly the engine and middleware your potential employers are currently using, you'll have to pick all that stuff up on the job anyway. That said, C++ and DirectX might be a good start if you're interested in Win32 PC games (which I'm not). Consoles are more varied, but the Unreal Engine is popular, widely portable, and there's some sort of student version available.
Most game development today isn't focused on core engine development. Middleware is increasingly used and scripting and data driven approaches are becoming the norm. In many games, there's significantly more non-programming labor than programming. (Which didn't used to be the case.)