"The boys' hats are big."
Translation:Les chapeaux des garçons sont grands.
This case is called "complément de nom". It is constructed with definite article + object possessed + de + determiner (definite article, adjective possessive, etc) + owner
Practically speaking, the French do not have the possessive construction with [owner + apostrophe + thing owned] the English use.
In addition, "de-le" is contracted in "du" and "de-les" is contracted in "des" (therefore "des" here is not the undefinite article, plural of un/une).
- Le chapeau du garçon = the boy's hat = the hat of the boy
- Le chapeau des garçons = the boys' hat = the hat of the boys
- Les chapeaux des garçons = the boys' hats = the hats of the boys
- Le chapeau de la fille = the girl's hat = the hat of the girl
- Les chapeaux des filles = the girls' hats = the hats of the girls