I have (what I think is) a better idea: Skip it...as part of your trip. Do it when you get back home. (I'm assuming home is somewhere in North America.)
Any activity that involves getting yourself off the ground and playing around in the sky costs more than a little money. Paragliding, skydiving, flying small airplanes, hot air ballooning, and (especially) learning how to do any of these things yourself...none of them are cheap, even if you're just riding along for a few minutes with someone qualified.
You can do any of these things at home, or you can do them while on your once-if-a-lifetime trip to [insert name of lovely place in Europe here]. For most people, it's the experience of being up in the air (perhaps jumping out of a plane, perhaps hanging from a balloon, whatever) that's going to thrill you, that's going to be the thing that feels different and special. Believe me, as you plummet from 10,000 feet up and fall to the ground like a proverbial rock strapped to some stranger's chest, the experience is not going to be terribly different if the ground that's rushing up to meet you is ground that's in Tuscany or Tuscaloosa....it's the thrill of doing it that will matter to you, not so much where you do it. Any time you are leaving the ground for a while, you're paying more than a little for the magic of defying gravity. But where you do that can make a big difference in how much it costs.
Few people realize that the USA/Canada is the least expensive place in the world for average folks to get off the ground and get in some sky time. There's a variety of historical, cultural and administrative reasons for this, but it's absolutely true: getting up in the air in Europe costs a lot more than in the USA/Canada. Do the exact same thing in Switzerland or Italy or pretty much anyplace else in the world and you will pay more....way more than at home. In fact, people from Europe and China and everywhere around the world come to the USA for flight training because (to them) it seems crazy cheap here (and relatively speaking, they're right).
There's also the "opportunity cost." For most of us, I think the usable time we have to spend in Europe (or other foreign destination) is our most constrained resource. You can go paragliding pretty much anywhere, any time. That day you spend paragliding in Switzerland (for example) is a day you could have spent doing something else that you can only do in Switzerland: blowing alpenhorns or running-with-the-cows or whatever you might choose.
If you've always wanted to fly (however you envision flying), you should do it. But I'd do it at home, where it's way less expensive, where you won't be burning a precious day of your European trip, and where you'll have a lot more choices/options for how/where to do it.
Hope that helps. Blue skies and tailwinds, have fun.