Formal:
* Son frère a les cheveux châtains. (This is the most common and literal translation.)
* Son frère a des cheveux bruns. (This is less common but still correct.)
Informal:
* Son frère a des cheveux marrons. (This is the most common informal way to say it, and it implies a darker shade of brown.)
* Son frère a les cheveux roux. (This means "his brother has red hair" and is used for a lighter shade of brown that is almost reddish.)
For a very light shade of brown:
* Son frère a les cheveux blonds foncés. (This translates to "his brother has dark blonde hair".)
You can also use the adjective "brun" or "châtain" to describe the hair color without mentioning the brother:
* Les cheveux bruns.
* Les cheveux châtains.
The best choice will depend on the context and your desired level of formality.