Timing is the tricky thing here. Give the fries their first cooking before you get the mussels on, then give them their second as the mussels are coming up to the finishing line. Neither want to wait to be eaten, but the moules will last better than the chips. Check the mussels very carefully before cooking. Tap them on the side of the kitchen sink as you remove their beards and barnacles. If they refuse to close then chuck them away. Any cracked or chipped shells should go, too. Use large floury potatoes, such as Maris Piper, or, if you can find them, Arran Victory. Double frying is essential.