Actually, I have heard it pronounced more like ah-nay or Anna. I agree with the poster who said they prefer that pronunciation. I think if you want it to be said like that, you would spell it Anais, without the dots over the i.
― Anonymous User 6/18/2013
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It's my sister's name and yes, the S must be pronounced in French. Also, a famous perfume from Cacharel is named 'Anaïs Anaïs'.