What makes the Sandwich au Jambon Persillé unlike the rest of the ham shelf is that the filling is half jelly. Jambon persillé is a Burgundian terrine, the region it belongs to: coarse pieces of cooked ham set in a parsley-flecked, wine-laced aspic and sliced as a marbled block rather than a sheet.
That structure dictates everything. The terrine has to be cut in a thick slab, because a thin slice shears along the jelly and the marbling falls apart. It carries its own moisture and its own acidity from the wine in the aspic, so the butter underneath is not fighting salt; it is a cushion between a cool, faintly sharp filling and the wheat of the crust. The bread needs a firm crust and a sturdy crumb, since the filling is soft, wet, and heavy enough to slacken a weaker loaf. It is eaten cool, and best within a short window of being built, before the aspic warms against the bread. No pickle is wanted: the sharpness is already inside the terrine.
It is the most transformed reading of the canonical Jambon-Beurre: the same baguette and butter, but the ham rebuilt as a Burgundian parsleyed terrine, the jelly doing what a slice cannot.