A resumé for Italian readers is here:
Recently I bought a device in France and was not charged the TVA notwithstanding the purchase being made as final user. I guess I was lucky, but the site explicitly said TVA would not have been charged for shipping outside France. That raised some long forgotten memory about VAT exemption in intracomunitarian exchanges.
In case you are interested, the product I bought was a dental irrigator, produced by Broxo, sold through their "European shop" at eu.broxo.com.