Gigi is French girl's (nick)name, usually short for names like Georgette, or any others beginning with the letter G.
There was also a famous short novel by Colette with this name, which was made into a musical film. I happen to love the film and the book, although they are quite different. Gigi in this novel/film was a young Parisian girl who was being trained as a courtesan but whose proposed "keeper" ended up in love and marrying her.
I'm afraid I don't know "Extr@ TV series" so I can't be more specific.
Student or Learner