Chimene is not listed in the database but since it is French, the stress is on the second/last syllable, "shi-MEN". Shi-mean is certainly not the French pronunciation though it may be an American one.
It is as you know a French form of Ximena. But the meaning of Ximena is unclear. Ximena may be a female form of Simon, in which case it means "listening".
Not all name meanings which you find on internet or in baby names books are correct. Where did you read that Chimene is Greek and means "heroine"?
"You may give them your love but not your thoughts. For they have their own thoughts. You may house their bodies but not their souls, For their souls dwell in the house of tomorrow, which you cannot visit, not even in your dreams." (On Children by Kahlil Gibran)