Why not just keep the contacts in FM Pro and use FM GO on your mobile device to access a copy of it?
From a Google "filemaker osx contacts sync"
http://www.addressbookmanipulator.com/ is a $75 plugin for one user
http://www.twdesigns.com/freebies/filemaker_to_address_book.php a free applescript (may have problems in Mavericks)
One to 5 seats 99 €
Using MBS Plugin 3.2pr7 and newer you can access the address book on Mac OS X from Filemaker. You can query, create and edit records, both groups and people. So in this article we show you how to do certain tasks.
http://360works.com/filemaker-sync/ another plugin