plus: in Europe in a lot of countries it's simply forbidden to make open fire in the countryside.
Just like you're not supposed to (mostly it's forbidden actually) camp outside of campsites in a lot of countries.
Some countries DO allow free / wild camping (Scandinavia mostly), but most severely restrict the possibilities.
You sound like you're from the USA, please remember that a lot of Europe is far more populated then a lot of the USA.
I would take a small stove.
I guess my real question is: why would you want to cook over a campfire? I feel it's inefficient, not always possible etc.
(unless you mean to use one of those bushbuddy type stoves, but that's not open fire).
I would imagine any campstove is far quicker, cleaner (though not cheaper) then a campfire.