Chicken cordon bleu is a classic French dish that typically pairs well with light and fluffy starch, such as mashed potatoes, lightly toasted bread, or risotto. Depending on the recipe, you can also serve it with some kind of creamy sauce or gravy.  Rice pilaf is also a great accompaniment to chicken cordon bleu. It can be dressed up with different herbs and spices for an even more flavorful side dish. When served alongside steamed veggies like green beans or broccoli, this dish makes for a complete meal that's sure to please everyone at your dinner table.