Are you sure it is '코자네'? because there is no such word in Korean. However, I can interpret this as '코( an onomatopoeic word indicating someone is asleep)' and '자네(modified version of '자다'=fall asleep)

코~ 자네 means "Oh, She/He/it sleeps soundly!" 코 is onomatopoeia like 쿨쿨 = snoring, z-z-z 코 is used for baby, puppy or kitty. 자네 << 자(다) + 네 자다 : to sleep 네 : exclamation ending suffix denoting that the speaker found out something new.