In the US, we'd be more likely to say "store" than "shop" and more likely to say "clothing store" than "clothes" store. I would never say "Fashion store."
They are in the furniture shop. This is OK. We (Americans) would more likely say,"They are in the furniture store".
They are in the clothes / fashion shop.They are in the clothes shop.This is OK. We (Americans) would more likely say,"They are in the clothing store". We generally don't call it a fashion shop or store. Fashion is more of a concept. C