Talking about the Euro or Freedom Of Movement is boring. It would be more fun to talk about the utterly ridiculous and unreasonable demands the EU would never really ask for but just how far would you be willing to go.

What if the EU asked for the Elgin Marbles back? It's unlikely but actually it's an entirely logical request.

Changing to full metric. That's just logical to do in general.

We have to rename Pineapple to Ananas to match every other European language. Also pharmacies have to become "Apothecary" so it matches all the countries that call it some variation on Apotec, to make it easier to ask for medical help. And we need to use those funky animated green cross signs, it's not optional, it'll be mandated in law. Animated gifs of flashing green dots on the sign or no EU membership.

Switch to the Central European Time Zone.

Do DVD regions still exist with Blue Ray? There's not really PAL and SECAM anymore. There's probably a modern equivalent, switching top tier DNS server or something.

Anything else?