Peel and wash the potatoes. Halve the shallots and cut into wedges. Pluck the herb leaves from the stalks and chop finely. Clean the chili, wash, halve, remove the seeds, dice the chilli very finely. Mix herbs, chili and lemon zest with butter, breadcrumbs and salt. Lightly grease an ovenproof dish with butter. Place the fish fillets in the dish and spread the herb mixture over them. Cook in a preheated oven at 180 degrees (gas 2-3, fan oven 170 degrees) on the 2nd shelf from the top for 12-15 minutes.
Cut the potatoes into 3-4 mm slices. Heat oil in a pan. Fry the potatoes in it for 10-12 minutes over high heat while turning. Add the shallots 3 minutes before the end of the cooking time. Remove the fried potatoes from the heat and mix with salt, pepper, vinegar and olive oil. Take the fish gratin out of the oven and serve with fried potato salad.