By rights it should not work as a sandwich at all, and that is exactly the appeal of this curiosity. A quenelle is a Lyonnais dumpling: a light paste of pike, flour or panade, egg, and butter, poached so it swells into something between a soufflé and a fish mousse. Sliced and pressed into split bread, sometimes with a spoon of the sauce Nantua, the crayfish-butter sauce it is usually served under, it makes a sandwich out of a dish that is normally eaten with a fork off a plate. The region is Lyon, where the quenelle is a fixture of the bouchon table.
The craft is a problem the sandwich has to solve rather than a logic it follows. A quenelle is delicate and barely holds its own shape, so it is sliced thick and laid flat rather than mounded, and the bread does the structural work the dumpling cannot. A firm crust matters because the filling brings nothing rigid; too soft a loaf and the whole thing slumps. The quenelle is mild and rich, so a little of the sauce or a squeeze of lemon keeps it from going flat, and the discipline is to add only that. It is best within a few minutes of being made, while the dumpling is still set and the bread still has its bite, which is why it stays a counter curiosity rather than a packed lunch.
Variations stay on the Lyonnais table. The same bread takes a quenelle in sauce Nantua for the full crayfish richness, a plainer poultry quenelle in place of the pike, or a slice eaten with nothing but lemon for the lightest version. The Sandwich aux Quenelles belongs with the dishes the catalog groups under Plat-en-Sandwich, the regional specialties folded into bread. Its specific contribution is the improbability: a delicate poached dumpling asked to behave like a sandwich filling, carried entirely by the crust.