Hi Lydia, I’m no expert but I’m learning fast from my mistakes! You need to be VAT registered in any country where your stock is stored so if you go for Pan-Eu you need to be VAT registered in all seven countries where Amazon have fulfillment centres. The issue there is it is costly to use Amazon VAT services in several countries where you may not sell much. As a result I have gone down the alternative route of registering in just FR, DE & IT with the intention of sending stock directly to those three countries where I sell most and the other markets can be supplied from those centres using EFN. (So for sales in FR,DE & IT I only pay domestic fullfillment charges, if they send an order from FR to ES for me I pay a cross-border fee as well).
Make sure you are VAT registered before you try and send any stock to other coutries, particularly Germany, otherwise your account in those countries will be suspended. I made that mistake and have been locked out of Germany for six weeks so far still waiting for my VAT certificate to be granted.
Look closely at the Fullfillment By Amazon setting page found from the settings droplist on the top right of your seller central home page and make sure PAN-EU is not enabled and that the other settings (like Allow Inventory to be Stored in Other Countries) are apropriate for how you want to operate.