Marc Liyanage - Software - Mac OS X Packages - MySQL
I use dbVisualizer at work with Oracle. Very nice application -- the full version is only $70 or so. I noticed it claims to work with MySQL; some quick research supports this.
MySQL can be freely downloaded (open source).
Both dbVisualizer (Java) and MySQL apparently run quite well on OS X.
The combination of dbVisualizer and MySQL is nowhere near as user friendly as FileMaker, but I'm not sure it's beyond the comfort zone of a Microsoft Access victim. I may play with this on OS X a bit.