Is prince a proper noun

No, prince is a common noun, a Word for any prince of any kind.

A proper noun is the name of a specific person, place, thing, or a title; for example:

• Albert II, Sovereign Prince of Monaco
• Prince Edward Island, Canada
• Prince Global Sports LLC, Bordentown, NJ
• "The Prince of Tides", 1991 move with Barbra Streisand and Nick Nolte