You slice this filling, you do not spread it: the duck comes baked inside a pastry crust, a pâté en croûte rather than a terrine, and that is the distinction the whole sandwich turns on. Its name and character come from a specific Picardy preparation, pâté de canard d'Amiens. The duck is boned, seasoned, sometimes layered with a forcemeat and a thread of the bird's own liver, then sealed in a butter pastry and baked, so what goes onto the bread is a sliceable round with its own crust, not a soft grind. The build is a length of baguette, butter optional, and one or two slices of the pâté en croûte laid flat, with cornichons on the side for contrast. The region is Amiens.
The logic follows from the en croûte construction. Because the duck is already wrapped in pastry, each slice carries its own edge of baked crust, which means the sandwich has structure inside it as well as around it: the baguette holds the assembly, but the pastry ring keeps the duck reading as a composed slice rather than a smear. Duck is darker and more savory than pork, with a deeper, almost gamey length, so the sandwich runs richer than a country-pâté version and rewards the same restraint. Butter is barely needed because the pastry already supplies fat; a cornichon or a film of sharp mustard does more useful work, cutting the duck's depth and resetting the palate. The bread wants a firm crust to frame the slice, and the pâté is best cut thick enough that the duck and its pastry stay distinct rather than collapsing into the crumb. Thin slicing wastes it; an honest cut shows the layered cross-section the preparation is built to display.
Variations stay close to the Picardy charcuterie idea rather than leaving it. The same bread takes a plainer duck terrine without the pastry, a pâté enriched with a vein of liver for more depth, or a slice served alongside a leaf of frisée for a green, faintly bitter note against the fat. Each is a small adjustment of one rich, sliceable thing, the bread held constant. The Sandwich au Pâté de Canard d'Amiens belongs with the spreads and terrines the catalog groups under Baguette Pâté, and its specific contribution is a pastry-wrapped duck slice that brings its own crust to the sandwich.