The Thieves Guild of New Orleans was set up at the same time as the Assassins Guild by the External Candra. They acted as her private thieves and payed tithe to her every seven years to gain the Elixir of Life. They also hunted for anything pertaining to the 'Old Kingdom' because of the Guild Prophecies.
They later broke away from Candra, but still follow the Guild Prophecies to a certain extent. It was these prophecies that led to Jean-Luc LeBeau to step down as Guildmaster and hand the Guild over to Remy.
The hierarchy consists of a Guildmaster and a Council which is made up of one member from each 'family' within the Guild.
X-Men: The Animated Series
In the episode X-Ternally Yours, much of history remains the same although there is no mention of Jean-Luc Lebeau or any guild prophecies. Although not many of the guild members are seen or mentioned either.
In the episode Cajun Spice, not much is known about them other than them being rival guild to The Rippers (this version of The Assassins Guild).
Wolverine and the X-Men
Here they are mention in episode 6 of the first season titled Thieves Gambit. Although there is not much know about them and it is unclear who the members are other than Gambit.