The other answers here are "correct", but there's something to note. Even if you implement the bridging tables, you'll need to do more. I.e. say there is a movie that had a certain director for a period of time, and then changed, and so on and so forth.
The point is, you need to determine the scope of your application (in this case and in general). What types of relationships will it handle? Once you decide that, then you can implement an appropriate structure (that is, your suggested structure may be "correct" for a very small-scoped project, but not for another type).
What I'm saying is, determining the scope can help you decide if your implementation is correct. Sit down and decied what, exactly, you're using this project for then take the appropriate route (which will probably be the relational tables).