The installation is bugged in multi-user environments. The package will only install to the /Applications folder, and so requires administrators' privileges. However, installing this way denies other users access to a critical folder in the app contents, causing the app to crash on launch when run from any account other than an admin's. The way to fix it is to:
1) Right-click the freeciv.app and choose Show Package Contents
2) Get Info, and authenticate to modify the permissions
3) Add the user account you'll be playing the app from - give that user Read-only permissions
4) Apply the new permissions to all enclosed items using the drop-down menu
And you're done. Now, assuming you installed freeciv from an admin account, copy the ~/Documents/Freeciv folder to the same location in the user account you intend to use to play. You'll then have to modify the permissions:
1) Right-click the new Freeciv folder
2) Get Info, and authenticate to modify the permissions
3) Add the current user, assign Read & Write permissions, and make this user the owner
4) For good measure, delete the System and Admin users
5) Apply the new permissions to all enclosed items using the drop-down menu
And you're done. The game should launch and play without problems now (well, you'll still have to contend with the god-awful UI, but, hey, it's a free game after all!)