Can you eat brie when you are breast feeding?

Yes
It's safe to eat whilst you're breast feeding, though it can affect you it is unlikely to affect your baby.
Brie /brie/ is a soft cow's milk cheese named after Brie, the French region from which it originated (roughly corresponding to the modern département of Seine-et-Marne). It is pale in color with a slight grayish tinge under a rind of white mold. The whitish moldy rind is typically eaten, the flavor quality of which depends largely upon the ingredients used and its manufacturing environment.
Soft cheeses include cheeses with a higher moisture content as the factor that controls cheese hardness is moisture content, which depends on the pressure with which it is packed into moulds, and upon aging time. Semi-soft cheeses and the sub-group, Monastery cheeses tend to be bland in flavour. Some well-known varieties include Havarti, Munster and Port Salut.