FileMaker and MySQL are very very very different. Not the least of which is that FileMaker typically runs on your computer, not on a webserver. Zen Cart is a website application which runs on webservers, which are typically equipped with MySQL, and thus uses MySQL for all its data management. Most database-driven website applications will not work from a FileMaker database, and NONE of them will work with the database on your home computer directly.
Using FileMaker to store AND access your database data is a completely different concept than using a web-based application to access data stored on a webserver database.