Jeanette is at a stalemate; if she gets close with Claude, she loses her sister. If she wants to keep being friends with Athy, she can't reveal her identity. An orphan girl who dreams of a family but will never be able to get her own. Jeanette is starting to realize that she can't have both Athy and Claude.
At the end of this conflict, I believe Jeanette will give up on her dream to allow Athy to be happy. She'll still be a noble for sure but it's still a sad end for her.