The Crêpe Beurre-Sucre is the version of the sugar crêpe that admits a second ingredient. Where the Crêpe au Sucre is bread plus sugar, the Beurre-Sucre adds a thin slice or a small knob of cold butter, laid onto the hot crêpe just before the sugar is dusted over the top. The butter melts into the residual heat of the surface, the sugar partially dissolves into it, and the result is a buttered, lightly caramelised film across the inside of the fold. It is the canonical French street-cart crêpe, the one you order if you want a sweet crêpe but find the plain sugar version a little too austere.
The technique depends on the butter being cold and the crêpe being hot. A pat of beurre demi-sel (the slightly salted Breton butter is preferred) goes on first, the sugar is sprinkled over while the butter is still in the process of melting, and the crêpière folds the crêpe before the butter has fully liquefied. By the time the fold is finished and the crêpe is on the paper cone, the butter has melted into a thin slick distributed across the interior surfaces, and the sugar has formed a soft, granular crust where the butter is most concentrated. The first bite is butter and warmth; the second is the slight chew of partially dissolved sugar; the rest is the crêpe itself, which on a good cart is thin enough that you can read print through it before it goes onto the iron.
The salt in the butter is what holds the whole thing together. Unsalted butter produces a sweeter, blander crêpe; demi-sel butter produces a sandwich-like balance between the salt of the fat and the sweetness of the sugar. The Crêpe au Sucre is the unbuttered cousin and trades richness for purity; the Crêpe au Caramel Beurre Salé takes the butter-and-sugar idea and reduces it on the stovetop into a sauce, producing a slightly more dessert-like version of the same impulse. The broader Crêpe & Galette Salée tradition covers the savoury buckwheat side of the family and the more elaborate sweet fillings, and the Beurre-Sucre is the form that most cleanly bridges the two: a sweet crêpe that takes salt seriously enough to be eaten by adults at any hour.