Don't own a Mac, but I think I've seen posts here that indicate that users were able to import data from the address book into FileMaker. Can you export data from Address book into a text file? If so, you can then import from the text file into FileMaker. You might also check for third party produced plug ins. Don't know of one off the top of my head, but there may be one out there that supports integration with the Address Book.
It is puzzling, Bento does it, bees do it, why not Filemaker?
A $75 Plugin - Exchanges data between FileMaker® Pro and Apple's Address Book.
FileMaker- Quick OS X Address Book importing without plugins
free but not elegant
Exporting Contact Information From Mac OS X Address Book or FileMaker Bento
Once you have entered information into the Mac OS X Address Book, there is not a straightforward and easy way to get it out. There are two built-in Export options: “Export as vCard” or “Address Book Archive”. Neither is terribly useful or easy to access like an Excel file. vCards can be read by some contact management applications and the archive is primarily for use as a backup.
The closest hope I found of a good exporter is “AB2CSV” or “Address Book to CSV Exporter” a 99 cent Mac OS X utility available from the Apple App Store that allows you to export your own Address Book in a CSV or VCF file. Unfortunately, the files this utility provides are largely unusable and not even easily recognizable by Excel. Phone fields with custom labels get exported strangely and Notes fields have issues because they are multi-lined. You might give it a try but I was not happy with the results.
FileMaker Mac OS X Address Book and iCal Import
December 24, 2010
This sample database can be used by FileMaker developers to help create a customized solution. It is provided free of charge.
Utilizing Bento and FileMaker 11 this database will allow you to easily import Mac OS X Address Book Contacts and iCal Calendar Event/Task into FileMaker. It automatically maps all the appropriate fields.