The founder of the “Girls Gone Wild” videos defied a federal judge Thursday, calling him a “judge gone wild” and refusing to surrender to U.S. marshals on a contempt citation.

U.S. District Judge Richard Smoak ordered Joe Francis into custody after settlement negotiations soured in a lawsuit brought by seven women who were minors when Francis’ company filmed them on Panama City Beach.

The 34-year-old Francis, who makes an estimated $29 million a year through the videos of girls exposing their breasts, ...