As Jun-san said, talking about her ability, it would be はなせません, it sounds more natural to us. However, if you talk about something like this: "though she is Spanish, she doesn't speak Spanish", it's はなしません.

Thanks y'all!

Totally correct

Yes. Your original is grammatically correct. does not speak: はなしません can not speak: はなせません

Thanks! Back to the grammar book then!