Crossing from mainland France can be another story, and I wonder if a charter company would let you do that? If you leave from the right spot, it's only about 100 n.m., so it makes for a nice overnighter. But watch your weather window carefully. On our crossing, we got thumped by a Force 8/9 Mistral that generated the severest seastate conditions I've ever experienced. And we were in a much heavier design than the typical charter boat. Even if the weather's fair, the Ligurian Sea is a very busy patch of water -- keep a careful watch for ships and ferries.
Good luck to you!
Edit: P.S. If you only have a week, consider chartering in Corsica and skipping the crossing from France.
It certainly IS possible to charter in one of the Mediterranean ports and cross to Corsica. But I heartily agree with John's last recommendation. I have never done it, but friends who have crossed from the Cote d'Azur have been hammered going or returning. It is a long crossing and the weather can be violent.
We chartered out of Ajaccio and visited the west coast as far north as Calvi. I have visited Bonifaccio on a crossing from Sardinia. Bonifaccio is a
one-of-a kind port.
Another option is to charter in Sardinia and cross to Corsica. Porto Rotondo is very well developed for chartering, and northern Sardinia makes for great cruising.