
Max M. answered 06/29/19
Harvard Literature major with 20 years of coaching writers
Yeah, Shakespeare certainly knew his classical history and mythology, and I doubt the name Paris was an accident.
In terms of the significance, there are a couple of ways you might go. The connection you drew is probably the strongest--Paris's love for someone else's wife leads to his own death.
Also consider this: Paris of Troy's love for Helen sparked a 10-year war. Paris of Verona's love for Juliet (indirectly) ended a generations-long feud.