Forêt vs. bois
In French, both forêt and bois can be translated as forest or wood, but they are not used interchangeably. The main difference between them relates to size, density, and context.
Forêt
A1A forêt refers to a large, vast, and often dense expanse of trees. It is the standard word for a forest in its grandest sense. These areas are often wild, may have an official name and administrative status (e.g., a national forest), and cover a significant territory.
La Forêt Noire se trouve en Allemagne.
(The Black Forest is located in Germany.)
Nous avons fait une longue randonnée dans la forêt domaniale.
(We went for a long hike in the state-owned forest.)
Les pompiers luttent contre un incendie de forêt.
(The firefighters are battling a forest fire.)
De nombreux animaux sauvages vivent dans cette immense forêt.
(Many wild animals live in this immense forest.)
La déforestation menace les grandes forêts tropicales.
(Deforestation threatens the great tropical forests.)
Bois
A1A bois is a smaller wooded area than a forêt. It is best translated as woods, a wood, or a grove. A bois is generally more contained, less vast, and often found closer to inhabited areas or on private property. Importantly, bois is also the word for wood as a material.
Il y a un petit bois juste derrière le village.
(There is a small wood right behind the village.)
Les enfants construisent une cabane dans le bois.
(The children are building a treehouse in the woods.)
Le Bois de Vincennes est un célèbre parc à Paris.
(The Bois de Vincennes is a famous park in Paris.)
Nous allons chercher des champignons dans le bois de mon oncle.
(We are going to look for mushrooms in my uncle's woods.)
Ce meuble est fabriqué en bois massif.
(This piece of furniture is made of solid wood.)
Summary
In essence, the key difference is scale. Use forêt for a large, expansive forest. Use bois for a smaller, more localized area of trees, typically called the woods. Remember that while a forêt is always a large wooded area, a bois can be a small one or refer to the material wood.