Corsica and Sardinia are separated by a few miles and it seems strange to me that one belongs to France and the other belongs to Italy. Corsica is "closer" to Italy than France. How did this arrangement occur? Did Italy ever possess both islands? Did France? Have these islands been a source of strife for the two countries in the past?
Corsica and Sardinia were once under the control of the republic of Genoa. A united Italy briefly controlled Corsica during 1942-1943, but they controlled Sardinia since the unification. The Corsicans revolted against the Republic of Genoa in the late 1700's and won. The French bought the rights to the island from Genoa and invaded the Island in 1768 and eventually annexed it. Although, surprisingly the Corsicans put up very stiff resistance.
Control over the island wasn't really disputed until Benito Mussolini rose to power in Italy and began to speak of uniting all the lost Italian lands. This included Malta, parts of the Dalmatian coast, Nice, the Italian part of Switzerland, and the island of Corsica. They gained Corsica when "Case Anton" was enacted by Nazi Germany in 1942. The Germans and Italians occupied all of the European territory of Vichy France, and the Italian occupation zone included a small amount of territory in southern France and the Island of Corsica.