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Coupe vs. découpage

While both coupe and découpage in French relate to the idea of cutting, they are not interchangeable. Coupe is a general term for a cut or style, whereas découpage refers to the specific process of cutting out shapes or dividing something into sections.

Coupe

A2
The word coupe is a very general term. It can refer to the result of cutting, such as a haircut, a slice of food, or a wound. It can also describe the style or shape of an object, like clothing. Finally, it can refer to the general act of cutting, especially in abstract contexts like budget cuts.
J'aime beaucoup ta nouvelle coupe de cheveux.
(I really like your new haircut.)
La coupe de ce manteau est très moderne.
(The cut of this coat is very modern.)
Le boucher m'a préparé une belle coupe de bœuf.
(The butcher prepared a nice cut of beef for me.)
Le gouvernement a annoncé des coupes dans les dépenses publiques.
(The government announced cuts in public spending.)
Attention, tu as une petite coupe sur le doigt.
(Be careful, you have a small cut on your finger.)
La coupe du bois demande beaucoup d'efforts.
(The cutting of wood requires a lot of effort.)

Découpage

B1
The word découpage refers to the specific process of cutting something out from a larger whole, often with precision. It is commonly used for arts and crafts, carving food, or dividing something into distinct parts or sections, such as film scenes, book chapters, or geographical territories.
Les enfants adorent faire du découpage avec du papier coloré.
(Children love doing cut-outs with colored paper.)
Le découpage du poulet rôti est tout un art.
(Carving the roast chicken is quite an art.)
Le réalisateur travaille sur le découpage technique de son film.
(The director is working on the technical breakdown (shot list) of his film.)
Le découpage électoral de la région a été très controversé.
(The electoral redistricting of the region was very controversial.)
Le découpage de l'article en plusieurs paragraphes le rend plus lisible.
(The division of the article into several paragraphs makes it more readable.)
Ce joli flocon de neige est un découpage que ma fille a fait.
(This pretty snowflake is a cut-out that my daughter made.)

Summary

In short, use coupe for a general cut, a slice, or a style (like a haircut or the fit of a garment). Use découpage for the specific action of cutting out shapes (like in arts and crafts) or the methodical division of something into sections (like carving a turkey, defining electoral districts, or planning film shots).