The Sandwich Steak Haché is the French ground-beef sandwich, and the distinction worth holding onto is that it is built around a steak haché, not a hamburger patty. A steak haché is seasoned ground beef formed into a thick disc and cooked like a small steak, ordered by doneness the way a cut of beef is, often left rosy in the middle. Put it in a split baguette or a sturdy roll rather than a soft bun, dress it sparely, and you have the French reading of beef-between-bread: closer to a bistro plate folded into a loaf than to fast food.
The craft follows from treating the patty as steak. Because the beef is cooked to a chosen doneness and seasoned to be eaten on its own, the build does not need to drown it. The supports are restrained and functional: a stripe of Dijon or a film of butter to bridge the meat to the bread, maybe a slice of tomato or a leaf, sometimes a spoon of cooked onion, occasionally a slice of melting cheese laid on while the patty is still hot. The bread does real structural work here, because a thick patty pushes back and a soft bun would collapse under the juices, so a baguette with a true crust or a dense roll holds where a brioche bun would surrender. The timing is steak timing: best within a few minutes of the pan, while the center is still warm and the bread has not taken on the rendered fat and gone heavy.
Variations move toward the bistro rather than toward the burger chain. A version with a shallot-and-red-wine reduction already on the bread reads like bavette treatment applied to ground beef. An à cheval build sets a fried egg on the patty with a barely-set yolk. A pepper-sauce version finishes it like a steak au poivre. Where a melting cheese is added it stays one slice and is allowed to be quiet rather than the point. The frame is constant: a seasoned ground-beef disc cooked to doneness, a single sharp or fatty bridge, a bread strong enough to hold it. It belongs with the roast and beef sandwiches the catalog groups under Baguette Rôti / Bœuf, and its specific contribution is the patty handled as a small steak, which is what separates it from every soft-bun build it superficially resembles.