What do you mean by the default character set in X? X applications like browsers can work with several charsets, usually configured from within the program. If you mean keyboard layout, you can modify /etc/X11/xorg.conf and add Greek. For console, you can try to put into /etc/profile (this is for bash) commands like
and so on. It may not be exactly as I stated above, please make a Google search and you will find. Finally, you may need some console fonts and Greek language support for the console (compiled into the kernel?). Utf-8 may also do, as it covers almost all the characters around.
Sorry for the vague answers, I hope they will be useful to you.
Also, AFAIK, Utf support (in menus, window title bars etc) has been added to fluxbox recently, so you may need the 1.0rc2 package for that , please check the fluxbox documentation.