Learning more languages will only be to your advantage. Even if nearly all pro engines use--or should use--scripting and/or extensive tools for designer ease-of-use, you're correct in that it helps greatly to have a project that you have specifically worked on. Even if your interviewer doesn't pay attention to your projects (which is already unlikely,) working on even one personal project will be a huge learning experience.
For designers and artists, the portfolio is arguably even more important, since you can't take programming tests or have straightforward tech interviews. So, I'm not saying that you should freak out and learn everything there is to know about C++.
Rather, you should be able to show a few games that have good design potential (think small, clear game concepts like Limbo or Portal,) whether you developed them yourself or you made them using Flash. Use coding as a tool, not as your primary weapon. Make sure they're easily accessible on your site with gameplay videos, screenshots, and available downloads.
Above all else, polish everything you make, no matter how small or what kind of project you have. If programming is about robustness and usability, then designing is about fun (people often forget this) and showing that you can really nail the details.