Technically Nice was never a part of Italy. Nice was most of the time part of the Duchy of Savoy (later called the Kingdom of Sardinia when the Duke of Savoy also became the king of Sardinia). Nice became French in 1860 while Italy was formed in 1861.

What used to be the Duchy of Savoy is now split between Italy and France.

EDIT: A map of Savoy in the 16th century: https://en.wikipedia.org/wiki/File:Savoy2.png