I don't know, but I'd be surprised if she did. In fact, I don't think Charles speaks Welsh either. Keeping things in perspective though, only 20 % of population of Wales itself speaks Welsh as first language.
BTW, I know Charles got an A-Level in French at school with a grade C (not very stellar then), so I assume he must speak at least basic French . William's A-Levels were in geography , history of art and biology with grades A, B and C respectively, which makes him one of the best students in the Royal Family in recent times (compared e.g. to his father, brother and uncles), but far from academically gifted.
Also, on the topic of consorts, Camilla left school with O-levels only. In other words, she didn't even get a qualification that would have enabled her to apply to a university. Compared to Camilla, Kate's qualifications (a bachelor's degree in art history) are "outstanding".