That first point makes sense, though I think its a bit goofy to have them split.

Also no worries about the history! Long story short, it used to belong to the Republic of Genoa who had a very goofy looking map,

A few hundred years later Corsica rose up against the Italians and the Italians requested the French militaries help. After the conflict ended the French just took it as repayment for their help.