Most of the campgrounds I have experienced in Europe (Italy, France, Germany) are pretty civilized affairs. I was discussing this with my significant other just yesterday and extolled the virtues of European campgrounds, replete with restaurants (plural), bars, and wonderful amenities. As you surmise, most of these sites are not in desolate and remote places, although I am sure those exist.
One of my dreams is to do a long term lease of a vehicle, pack it with a reasonable selection of camping gear, and to go native with the mass of free-spirited adventurers. I have done it in a motorhome with wife and two young kids, and it truly was a grand way to visit places. Many of the campgrounds are in resort destinations like beaches, while others are on the outskirts of cities and towns. There are usually bus routes that serve the campgrounds or, in one instance, a boat route on the lagoon in Venice (Camping Fusina). I have camped on a hilltop in Bologna, in a volcano crater (Solfatara) in Naples, across the river from the Pont D'Avignon, and on a quiet bank of the Seine near Paris. Check out some of the sources below to get you in planning mode.
Edited to add that stringing a hammock style tent between trees is probably not encouraged and that free standing tents are probably the way to go. In truth, REI could probably outfit you pretty well and you wouldn't have to go uber-lightweight (and therefore uber-expensive) because you don't have to schlep it much.