I have never read F. Scott Fitzgerald's The Last of the Belles. However, my guess would be that she is not a common or average person. This is based on my belief that Jane used to be a very common name and the context of the rest of the sentence. That's my best guess.

looking at the clues the other three users have provided to me. "no Jane" = she is no average ordinary girl. She is a society girl. the best clue being provided by Jeffrey who gave the books title as "the last of the bells. belles are society girls. from amazon books google search. Inspired by Fitzgerald’s own courtship of his future wife Zelda, ‘The Last of the Belles’ centres on the Southern beauty Ailie Calhoun from Tarleton, Georgia, who finds herself the object of attention of all the officers at a nearby army base, including the narrator, Andy. A wistful and melancholy exploration of unfulfilled dreams and lost youth, the story is considered one of Fitzgerald’s finest pieces of short fiction. belle definition a beautiful girl or woman, especially the most beautiful at a particular event. the term was often used amongst high society people at their grand balls.

As a third alternative it could refer to the "Jane" character created in the Second World War to boost morale. Details here https://en.wikipedia.org/wiki/Jane_(comic_strip) I wonder which of us is right

'Jane' refers to Jane in the Tarzan stories. Jane is a woman who finds Tarzan and ends up living a very wild life in the jungle, with none of the amenities of modern life. So 'she's no Jane' implies that this woman can't do without those amenities, indeed she relishes everything that 'civilised' life has to offer. I hope that helps! Steve