Sicily was conquered by Charles I, Duke of Anjou in 1266. Following the Sicilian Vespers 1282, Kingdom of Sicily was split in two (and would remain so until 1816) with the continental part commonly referred to as Kingdom of Naples. Charles of Anjou continued to rule the continental part after the Vespers.

Another Charles of the same house became king of Hungary in 1312 and his descendants would rule Hungary until 1395.

Your claims about French rulers in 1350s Sicily seemed strange, so I went to check and the ruler is not French. Note regarding the game: the last possible start date in Crusader Kings 2 is the 1st of January 1337. Since Charles of Naples starts with a claim on Sicily, he might have conquered it by the 1350.

The Anjous also ruled as kings of Poland, Croatia, Albania, princes of Achaea, despots of Epirus and emperors of the Latin Empire.

CK2 has a pretty accurate title history.

edit: thought I might add - all historical characters in Crusader Kings 2 have an info button next to their age that leads straight to their Wikipedia page.