There are no private servers for FFXI. Square-Enix guards their server info much better than Blizzard does.
Some people have tried making emulated FFXI servers, but the best anyone has ever done is gotten a completely black area to load for a few seconds. No environment, no character models. You could talk in /say in the chatlog, but the was pretty much it. And it kicks you off after only a few seconds.
They're still working on it though. Here's their site:
