Martin was born in Lindfield, New South Wales, to a French mother and an Australian father, both academics who met at the Sorbonne. She has one brother. As a child, Martin was fascinated by the vintage clothing parades occasionally thrown by her Australian grandmother and her church friends. She would beg her parents to take her to the Victoria and Albert Museum so she could dig through the costume section. Her mother taught her to use a sewing machine at age 6, and by age 15 she was creating her own patterns in order to make herself dresses. In an interview with Tory Burch, Martin mentioned "The Wizard of Oz" and "Gone with the Wind" as her childhood inspirations for her love of film and design.