This will require Titanium Backup (free from Market) and ROOT.
1.) Place contents of "FFIII v1.0.1" into /sdcard/TitaniumBackup (contents only, not the folder.)
2.) Place the FOLDER com.square_enix.android_googleplay.FFIII_GP into /sdcard/Android/Obb (you may need to create the Obb folder.)
3.) Place the Lucky-Patcher app on your sdcard.
4.) Launch Titanium Backup and restore app + data of FF3.
5.) Install Lucky Patcher apk.
6.) Run Lucky Patcher, grant Root privs, select FF3 > Open Menu of Patches > Remove License Verification! > Auto True (top option.) This may say it only achieves partial success (70%) for me, but it works.
Launch and enjoy.