I have tried a Wine wrapper I downloaded, but it's probably out of date because when I try to run the game I get a black or white screen. I'm on OS X Yosemite. If anyone has the GOG version that was cancelled a while ago, or has a way I can get it going, I would really love it. I have latest version of Wine and the Windows Fallout game (GOG install version). Thanks for any help. Here's the wrapper I downloaded: http://portingteam.com/files/file/7252-fallout-1
I wasn't able to run Fallout in Wine on OSX (10.11, El Capitan) either. And as stated in the Wine wiki entry for Fallout 1, the game is not working on Mac.
You may try to install VirtualBox, setup an Ubuntu 14.04 (both are free) and try the app in there. If it's not working you have to get a Windows license and setup a Windows virtual machine with VirtualBox.