The Sandwich Aiglefin Fumé is built around smoked haddock, and the fish arrives with a character that decides everything else. Aiglefin fumé is haddock that has been cured and cold- or hot-smoked, leaving the flesh firm, pale gold, and carrying a clean smoke over a mild white-fish base; the hot-smoked version flakes into solid lobes, the cold-smoked stays denser and is sliced or broken into sheets. In the sandwich it goes onto a sturdy split loaf, often buttered, with the smoked fish as the lead and a soft, mild partner against it rather than anything that fights the smoke.
The logic follows from the smoke and the leanness. Haddock is a lean fish, so it brings little fat of its own, and the cure adds salt and a smoky edge that needs softening rather than amplifying. That is why butter or a soft fresh cheese tends to sit underneath it, supplying the richness the fish lacks and rounding the smoke, while a few drops of lemon and a turn of pepper lift it without crowding it. The slicing or flaking matters: kept in generous lobes the fish stays moist and the smoke is measured; shredded too fine it dries against the bread and the smoke turns sharp. The crust has to be real, because flaked fish gives the sandwich no structure and the loaf has to hold the shape. It eats cool and clean, firm rather than melting, a quiet sandwich whose whole interest is the smoke against plain wheat.
Variations stay within the smoked-fish shelf. A version with whipped fresh cheese and chives leans soft and Northern European; one with a few slices of cucumber or a leaf of frisée adds a cool, crisp counterpoint; a poached-then-flaked build is moister and milder than a hard hot-smoked one. Each holds the smoked haddock constant and changes only what cushions it. The Sandwich Aiglefin Fumé belongs with the fish sandwiches the catalog groups under Baguette Poisson, the tradition that runs from oily tinned fish to smoked river and sea fish on bread and butter. Its specific contribution is a lean smoked fish that needs a soft, fatty partner to keep its cure from running the whole sandwich.