So she's a horrible person. Many people are. Is that relevant to her case in any way? You say she's been badly wronged. Does she somehow not deserve justice just because she's horrible? It sounds like you should perhaps compartmentalize.
What about free speech? You consider that an important right, I assume? The thing about free speech is it lets people say horrible things. And because free speech is important we have to defend their right to say horrible things. Dropping her as a client would, in a way, be punishing her for practising free speech. Okay I have no idea if France even guarantees a right to free speech. But still.
You've also stated she's basically crazy. You need to ask yourself if she's even capable of better behaviour. Can she even understand that it is wrong to say these things?
And finally, racism is a term often misused, I feel. I agree with the definition of racism that says actual discrimination needs to be involved, not just prejudice. Because, again, people really do have the right to hold hateful opinions if they wish. They do not, however, have the right to persecute or discriminate. It seems to me this woman is merely prejudiced and, while that is distasteful, do you really want to drop this client simply because she holds a different opinion to you? I could perhaps make an argument that you would actually be discriminating at that point.
Obviously it doesn't matter to me which choice you actually make. I'm merely trying to help you make one and I got the feeling you'd like to keep her as a client but were struggling to justify it so I went that way with it. You could also consider giving her a final warning for her behaviour, letting her know any recurrence would result in you dropping her. Though again you have to ask yourself if she even CAN stop.
Good luck deciding!
“Today a young man on acid realized that all matter is merely energy condensed to a slow vibration, that we are all one consciousness experiencing itself subjectively, there is no such thing as death, life is only a dream, and we are the imagination of ourselves.” – Bill Hicks