WINEDLLOVERRIDES=dwrite=d wine ~/.wine/drive_c/Program\ Files\ \(x86\)/Fractal\ Audio/Axe-Edit/Axe-Edit.exe
The latest version of the script quonsar mentioned is available from Al Grenadine's AxeFX Archive. Current version is 1.04 (http://forum.fractalaudio.com/threads/axe-fx-ii-and-linux-again.79061/page-5#post-1263842).
@RafterRattler: Thanks for reporting. What version of Ubuntu do you use? Did you get to the prompt "Press [y] to accept the Fractal Audio Systems Axe-Fx Software License Agreement or press any other key to cancel."?
V1.04 - 17.10.2015
Added check if the script is executed with root permissions.
Added check if the Linux kernel version is sufficient and also
added information what functionality will probably be achieved in case a kernel
older than version 3.10 has been found.
Added version information option "-v".