Team Fortress 2 in space already exists, it's called Star Conflict and it is incredibly fast-pace and fun.
There's something for every playstyle and the ships are crazy customizable.

If it wasn't in the hands of the shittiest whale-hunting bunch of assholes in gaming, SC would be the undisputed champion of PvP spaceship combat.

The game needs a sequel with a larger scale, 25v25 minimum, and a major balance overhaul.