Ernestina Freeman in The French Lieutenant's Woman by John Fowles is what is known in literary terms as a "foil". This means that rather than being a fully-rounded character who is treated as interesting for herself, she merely serves as a contrast with Sarah Woodruff, the "French lieutenant's woman" of the title.
Ernestine is the daughter of a wealthy merchant, and at the beginning of the main narrative in 1867 is betrothed to Charles Smithson, the protagonist of the story. She is pretty, fashionable, and conventional. She is not at all mysterious, but instead is content with the traditional female role in Victorian society. In the novel she has two functions, first to highlight the difference between the traditional Victorian woman and the unconventional, mysterious beauty Sarah, and also to represent the narrow traditions that constrain Charles. The love triangle represents traditional family (Ernestine) on the one side and adventure, intellectual curiosity, and self-fulfillment on the other.