On the island of Corsica, there is a 125 mile trek called the Grand Randonnee (aka GR20). This red and white blazed route has 69,000 feet of climbing and descending, and the route typically takes about 11 days. The route is divided into 16 stages that are separated by huts that offer bunks and meals. It can be done in fewer days by choosing hut spacing. It is recommended to hike the trail southbound. It follows craggy rolling ridgelines and has some near vertical assisted climbs (built-in wires). Watch out for Le Cirque de la Solitude section which is a cliff that is crossed with chains bolted to the walls.
The trailhead starts about 8 miles north of Calvi. Corsica is accessible via ferry from Nice. Make sure to bring camp stove fuel to Corsica. To reach Corsica, try flying into Ajaccio. There is bus service to both trailheads. By the way, Air France and Air Corsica fly from Nice to all the airports on the island.
Camping is permitted in designated areas only, and there are huts along the route which provide lodging and supplies. At most, the huts with supplies would be 3 days apart.
The best map for the route is GR20: A Travers La Montagne Corse by Federation Francaise de la Randonnee Pedestre.
The best guidebook is GR20: The Corsican High Level Route by Paddy Dillion.