Mince vs. fin
Both fin and mince translate to thin in English when describing a lack of thickness, but they are used in slightly different contexts. While mince generally refers to a strict physical lack of volume or a slim body type, fin carries an added connotation of delicacy, small diameter, or high quality.
Mince
A2The word mince is used to describe flat solid objects that have little physical thickness from top to bottom or side to side, and it is also the standard term used to describe a person or animal who is slim or thin.
Le dossier est mince car il manque plusieurs documents.
(The folder is thin because it is missing several documents.)
Mon frère a toujours été grand et mince.
(My brother has always been tall and thin.)
Le mur est si mince que j'entends les voisins parler.
(The wall is so thin that I hear the neighbors talking.)
Elle a étalé une couche mince de peinture sur la toile.
(She spread a thin layer of paint on the canvas.)
Il a lu un livre très mince en une seule heure d'étude.
(He read a very thin book in a single hour of study.)
La glace sur ce lac artificiel est encore trop mince pour patiner.
(The ice on this artificial lake is still too thin for skating.)
Fin
A2The word fin also describes something thin, but it specifically emphasizes elegance, precise detail, delicate texture, or a very narrow diameter, such as fine hair, delicate fabric, or a sharp tip.
Ce vêtement de soie est transparent car il est très fin.
(This silk garment is transparent because it is very thin.)
Il utilise toujours un stylo à pointe fine pour écrire ses lettres.
(He always uses a pen with a thin tip to write his letters.)
Elle a des cheveux extrêmement fins qui s'emmêlent facilement avec le vent.
(She has extremely thin hair that tangles easily with the wind.)
Le chef cuisiner préfère couper des tranches fines de légume pour la salade.
(The chef prefers to cut thin slices of vegetable for the salad.)
Le cristal de ce verre à vin est particulièrement fin et fragile.
(The crystal of this wine glass is particularly thin and fragile.)
Ses doigts longs et fins couraient rapidement sur le clavier du piano.
(His long and thin fingers ran quickly across the piano keyboard.)
Summary
In short, you should use mince when you are simply stating that an everyday object lacks physical thickness or that a person's body is slim. Conversely, choose fin when the physical thinness of an object involves fragility, precision, narrowness, or a delicate texture.