In a saucepan over high heat, bring 2 inches of water to a boil. Add the green beans and carrot ribbons. Cover the saucepan and cook 5 minutes, or until the veggies are crisp-tender; drain.
Meanwhile, in microwave on high power, heat the apricot preserves 30 seconds or until it becomes liquid. Place the green beans and carrots in serving bowl; toss with apricot preserves, salt, and cayenne pepper to coat.