Yes, in the sense that the league office has control over how many teams are in the NBA, so similarly to a fast-food franchise you need to get the league's approval in order to create a new NBA team.
So, it's a franchise because you need authorization from the NBA in order to have an NBA team, the same way you need to talk to McDonalds the company in order to start one.
The NBA's probably got a better burger, though.