Where in Europe can I pay to fire guns or have military experience?

For Slovakia, you could consider the Bratislava Rifle Range:

Bratislava's premiere outdoor rifle shooting range is the setting for our most popular stag do activity. You can have a blast shooting a real Scorpion machine gun, sub-machine guns or a selection of handguns supervised by certified instructors. We guarantee you will love letting a fully loaded machine gun go off at the rock above the metal targets with unbeatable sound and smoke effects.

In Poland (Krakow), there's the Gun Shooting in Krakow option:

Our firing range offers you the chance to fire some of the world’s best know guns such as the infamous Kalashnikov, the AK47, a revolver, various pistols such as the Russian MCM Margolin and the Austrian Glock as well as a traditional shotgun.

and in Hungary, shooting near Budapest:

Heavy-duty guns and real firepower (like Kalashnikov AK47 and many more), you can experience the power in your hands, which is incredible.

In Slovenia, Shooting in Slovenia (some NSFW pics) offers the following description:

Shooting in Ljubljana for stag parties, is one of our best sellers. If you’re asking yourself, why? Then you obviously haven’t gripped a hardcore firing weapon, and blasted off a target board. The power of the gun sends a rush to the arms with a rigor of excitement….just holding this deadly gun, you have become a lethal weapon.

But stuffed if I can find anything in Croatia...

In Poland you can visit Wolfsschanze (Wolf's Lair), the place where Hitler stayed during the war against Russia. There you can see the older concrete buildings, but you can also fire some massive guns for not a lot of money.

From the Website about the site:

Suffering from lack of adrenaline? Want to test your sniper abilities? Visit our new shooting range in General Jodl's Staff bunker (number 17) here at the Wolf's Lair. Both adults and children are invited to test their abilities with airsoft replicas of historical WWII weapons and air-guns. Our shooting range is open daily, throughout the day. Visit us - such an opportunity doesn't come often!

But I'll leave the answer as it is, because from my personal experience, I can tell you that weren't airsoft guns...

And now some personal thoughts about this:

I'm not really happy about that. The problem is, it attracts a lot of "dubious" people that are not there to visit a historical site, but just to more or less celebrate this place and fire some guns.

A lot of hostels in the Baltic countries like for example the Naughty Squirrel in Riga or the Boutique Hostel in Tallinn offer AK47 shooting tours.

Also the Kiev Backpacker Hostel in Kiev, Ukraine offers such a tour.

From my experience a lot of hostels in the Baltic Countries, and Eastern Europe in general offer such tours. If not mention directly, they can surely guide you where to join such a tour.

The one Western European country that you may be able to find these kind of experiences in is Switzerland. They are one of the few European states that have sensible firearms laws, and you can generally shoot without too many restrictions or hassle.

Specifically, if you don't mind giving the AK47's a miss, there is a great underground range in Brünig:

http://www.bruenigindoor.ch/

There you will be able to use modern handguns and rifles in clean, well equipped, modern facilities. They have SIG P226 pistols and SIG 550 rifles available for hire. As long as you can demonstrate that you can handle both safely, you shouldn't have any problems in spending a few hours there having some fun!

Celeritas Shooting Club in Hungray is top shelf. It may look a bit dodgy, when you're driving towards it in the taxi, it's like a scene out of Hostel but it ended up being the most wonderful experience of the trip trying all the guns from pistols, shotguns to heavy machine guns. I got the shoot 'em all package. Sorry if this is too late but you could put on the list for next time mate!