Since PlayOnMac is the easiest way to run FH, I'd like to try and work on getting that running, if this doesn't help we'll go ahead and move on to creating a wrapper in porting kit/I'll let you use my crossover license.
Do you have an option to repair disc permissions? Launch Disk Utility, click on playonmac harddrive and click repair disk permissions.
If you don't, that's fine, moving on.
Click on your desktop, click "go" at the top of the screen, click computer, click your mac hard drive then click library (at least that's how I do it, if you simply have an option to go to library do that!)
See if you have a playonmac plist file and if so move it to the desktop.
Retry.
Lastly, try changing the install location. If you had it set to move to applications upon install, try just dragging the install onto your desktop and not moving to applications, or vice versa.
If there is no plist file or none of those solutions work, the last thing I'd recommend is restarting your computer and having it's preferences set to no items opening on startup. When it's all loaded up, right click on your playonmac app and select open (don't just click it.)
Sorry for the hassle, I'll help ya set up a wrapper if none of those work <3