The Tuxedo (2002)
introduction as "The Last Emperor of Soul"
a poster for the movie is seen
title seen at video store
A DVD vendor recommends the film to his customers
poster in projectionist's room
When Rachel is browsing through the videos at the fair, The Tuxedo is one of them.
Mentioned in the question
VHS tape on video store shelf.
among the early 2000s spy craze