You do realize that:
- your girlfriend is going to wear the ring on one of her fingers if she accepts it
- she is going to someday travel by commercial air in possession of the ring
- she is going to keep the ring on her finger when passing through the metal detector or body scanner
?
Right?
Do you have fingers? Do you have a pinky? Then put it on one of your pinky fingers. If you don't have a pinky, put it on one of your little toes.
You can put the ring back in its box when you clear security.
As for customs in Europe, since this is an item that will be left in Europe, if she accepts, then you should declare it.
Good luck with your proposal!