How to repair or back up external hard drive when disk utility can't repair it?
You could try to "mount" it via Terminal.

First, make a mount point:

sudo mkdir /Volumes/EXT_HD


Now mount (your device numbers may be different, e.g. /dev/disk2s1 — you can determine what it is as it will the the highest number when you issue the command ‘ls /dev/disk*’):

sudo mount -t msdos /dev/disk3s1 /Volumes/EXT_HD/


It might eventually show up in Devices in Finder.