It'll be a new adaptation. It would have to be new for today's American sensibilities. Gigi is based on the 1944 novella of the same name written by the French author Colette. In the movie musical, as in the book, Gigi is being groomed to follow other women in her family and become a courtesan. When we meet her, she's a lovable and energetic teen. She'd rather go out and play than take what seem to be social etiquette lessons from her wealthy Aunt Alicia. Aunt Alicia had several lovers -- important men who gave her expensive jewels and made her financially comfortable. But no one ever married her. Wealthy, kind Gaston loves spending time with Gigi and her grandmother. He's just ended a scandalous love affair. The bachelor's feelings for Gigi are purely platonic. Gradually, as she blossoms into womanhood, he falls in love her -- and she with him.
About Gaston being attracted to a very young female -- this was a European story. The age of consent in France in the early 1900s, when the story took place, was between 13 and 16. The Vincente Minnelli movie screenplay "cleaned up" the European sexual maturity of the novella so it could get an all-clear from the Hollywood censors. I'm sure the upcoming stage version will alter the screenplay even more to keep audiences from feeling creeped out..