Having no fixed recipe is what makes this the most local sandwich in France. It is a baguette and a cheese, and which cheese depends entirely on where the fromagerie is and what it ages well. In one place it is a wedge of slightly ripe brie spread soft against the crumb; in another it is dense Cantal cut thick; in another a sliver of a washed-rind cheese strong enough to announce itself across a room. The sandwich's identity is not a single flavor but a method: take whichever cheese the local maker ages well, give it good bread, and add almost nothing. What lifts it above a wedge of cheese folded into bread is the matching of cheese to handling, because a soft paste and a hard tomme want completely different treatment.
The build follows from the cheese's texture rather than a template. A soft, bloomy paste is spread, needs no butter, and benefits from a crust firm enough to give it structure it lacks on its own. A firm, dry cheese is sliced and laid in shingles, and a thin film of butter bridges its salt and the wheat in a way the dry-on-dry version cannot. A pungent washed rind wants very little around it and a sturdy crumb to keep from being overwhelmed. Across all of them the sandwich is best within a few minutes of assembly: the bread is fresh, the cheese is at room temperature so its flavor is open rather than fridge-cold and mute, and there is nothing in the build that will go soggy if it sits.
Variations are really just the choice of cheese, and the choice is a map of French dairy. A young Comté or a Cantal entre-deux gives a savory, sliceable sandwich; a soft Saint-Marcellin gives a spreadable one that wants only salt; a Loire chèvre on toasted seeded bread takes a touch of honey and walnut well. The Sandwich au Fromage belongs with the cheese builds the catalog groups under Baguette Fromage. Its specific contribution to that shelf is generality made into a discipline: not one sandwich but a frame that bends to whatever the nearest cheesemaker ages well, on the condition that the bread is worth queuing for and the cheese is allowed to taste like itself.