Recently i went for a short (1 hour) walk through the caves of Cocaliere in the ardeche in France. During the very touristic trip, although still quite interesting, we were guided passed two tents, from where the initial explorers searched the surrounding. The idea of being able to explore through a cave for more then one day seems quite tempting and adventurous. Is this possible while not being an experienced speleologist?
It looks like there are quite a few, with this page giving a good start.
Hölloch Caverns, Switzerland
Hölloch Caverns is the second largest cave system in the world and extends as much as 118 miles in length. There’s a basic touristy, light section, but guided tours and multi-day expeditions in the cave for advanced spelunkers are available as well.
Dan yr Ogof, Wales
This ten mile long cave system in south Wales is thought to go as far as 150 miles. It’s a major showcave and considered the greatest natural wonder in Britain, but also a favorite site for European cavers.
Ease Gill, England
The wide variety of caving routes and a stunning river passage, the main Drain, make this UK cave one of the top in all of Europe for spelunking. The longest system in the British Isles.
Plus others, but these sound like the longest.
Cumberland Caverns has overnight tours.
Finally you could ask on the National Spelunking Society site - yes it's US, but their cavechat forum has a lot of people who can give suggestsions based on skill and ability.