Virtually any "warm toned" neutral carpet will work with red/ terra cotta tones. Camel tones, warm beiges, ...but it also depends on your paint colors as well.

I would base my decision on the color of your walls and what you already have in your living room - couch, art, drapery. Beige, cream, grey, caramel, mocha, blend of two colors/subtle pattern would all work. If you could add a photo, it would help for people to make recommendations.