Corsica is great. Granite, wild tofani formations. Some of the "sport" is "sporty" but you can supplement with threads and a small rack of gear. Mont Gozzi, Restonica, Bavella... Presles. See the database here on the proj' for a little taste. St. Victoire, Calanques, Dolomites, etc etc etc. Gobs.
All great sugggestions! Also look into Meteora, Greece. It is almost all bolted climbing but it tends to be very run out! There are some routes there on the Spindal which climb like sport routes.
Rapping off of the Spindal, Meteora.
For my money and a relativly short trip I would go to the Dolomites. We climbed at the Cinque Torre which was amazing. Theres lots of sport routes there but with a great alpine feel. Plus you can stay at a refugi 100 yards away from the routes. We stayed at Refugi Sciotloi which had the best food we had in a 10 month trip to Europe. Plus if the weather sucks there is plenty of via ferrata and hiking.
Dolomites are great! Pretty much the most steep rock I've ever seen in a region. From my two weeks there I wouldn't call it a "sport" destination. There are lots of pitons and some bolts on the big routes, but all multi-pitch I did we had a rack for for. Every route kinda felt like an adventure climb too, with lots of route finding, funky protection and big lines.
I put my two cents in for the Verdon for multi-pitch sport. Stunning setting, with big lines. Kinda committing since you have to rap into the massive gorge to then climb out. Beautiful, tiny, quaint town of La Palud has many lodging options. Like a lot of european climbing, it would be pretty hard to climb here without a car.
For pure sport multipitch, it's hard to go wrong with Les Calanques. Just be aware that some of it is closely spaced sport, and some is more sporty. The guidebook is pretty clear, though, on what's what.