Bastien and Marie Laveau were lovers and Bastien impregnated her. Marie had to give her baby's soul to Papa Legba as her first exchange for Immortality.
Bastien was a house slave in the home of Delphine LaLaurie. When Delphine holds a soiree to present her three daughters to eligible bachelors in New Orleans, the youngest one, Marie Pauline, makes a lewd joke that makes the bachelors and her mother uncomfortable. She constantly glances at Bastien, who tries to avoid her gaze. After the party, Pauline manages to seduce Bastien, but is caught by her father Louis, who tells his wife.
An enraged Delphine beats her daughter for her choice in men, declaring that they will say Bastien forced himself on her, rather than the other way around; at which point, Bastien is brought to the attic and restrained. She makes a young slave place a hollowed bull's head over Bastien's head. His swollen bloodied mouth causes him to sound just like the Minotaur of myth.
After the voodoo queen, Marie Laveau, wreaks her revenge upon Delphine and the LaLaurie family, she finds his dead body still chained, his head still covered by the bull's.
Marie Laveau, now the proprietor of a hair salon, has shared her secret of immortality with her lover, but keeps him shackled. Due to ambiguous reasons, her lover has transformed into an actual Minotaur, his hands half-hoof and the once empty bull-head now acting as his actual head. She orders him to kill the newly disinterred Delphine. The hunt brings him to Miss Robichaux's Academy. There, Delphine hides as Queenie lures the beast into the greenhouse where she encourages the creature to mount her. It does with dire results. Fiona later decapitates the beast and mails the still-alive head to Marie's hair salon, ending the truce between Marie and the Salem witches. Marie performs a resurrection spell, sending an army of the undead to the academy.
After Marie Laveau dies, it is supposed that the Minotaur dies too.
Immortality - As a result of the cure from Marie, the Minotaur is not susceptible to human weaknesses, thus being immune to all aging, disease, and death.
There seems to be a plot hole regarding his age; Marie Laveau claimed to be over 300 years old yet Bastien was killed by Delphine roughly 180 years before the events of Coven. As he died, he was clearly not immortal. However, Bastien is confirmed to be the father of Marie's child, which was her first sacrifice to Papa Legba for her immortality. This would mean that there was roughly a 120 year discrepency. It could be that Marie kept him alive through some prototype version of the potion she gave Delphine, or some other form of life extending magic, which prevented death via aging, but not via trauma.