The novel Frankenstein notes that Victor is Genevese by birth. (This means he is from or around Geneva and/or Switzerland. In his telling of his family's history, Victor states that he was born in Naples, which followed trips by his parents to Italy, Germany, and France.
Victor is very proud of his Genevese background. He states that his family is renowned in Geneva and that his ancestors have been recognized in the area for many generations as counselors and syndics (some affiliated with the court system).
Therefore, while born in Italy (Naples) which would make him Italian by birth, Victor states that he is Genevese by birthright and ancestry.
Victor Frankenstein was not actually born. He is a fictional character in the Novel Frankenstein by Mary Shelley. Frankenstein was given a truer character sense in that he attended real colleges, and traveled to real places. For example, University of Ingolstadt is where he attended college. Mary Shelley placed her novel of Frankenstein beginning in Geneva, Switzerland where he is "born" to a wealthy family. Victor found a love of science and medicine while in college and became fascinated with the idea of creating life. This is where the monster of Frankenstein fits into the picture, or should I say, book.