I have read several books on Princess Elizabeth, unfortunately all of them were in French.
If you can speak French or find translations, I would recommend the following:
- "Madame Elisabeth: la Princesse Martyre" ("Madame Elisabeth, the Martyr Princess") by Martial Debriffe
- "Une Sœur de Louis XVI, Madame Elisabeth" ("Madame Elisabeth, a Sister of Louis XVI") by Noelle Destremau
- "Madame Elisabeth, la Sœur Martyre de Louis XVI" ("Madame Elisabeth, the Martyr Sister of Louis XVI") by Monique de Huerta
- "Le Sacrifice du Soir, Vie et Mort de Madame Elisabeth, Sœur de Louis XVI" ("The Evening Sacrifice: The Life and Death of Madame Elisabeth, sister of Louis XVI") by Jean de Viguerie
Of those listed, my favourite are the first and especially the fourth ones (a really good read with plenty of pretty accurate and well-researched data), and the least favourite - the third one.
I've also come across this book on the Princess which you can read online: "La Vie de Madame Elisabeth, Sœur de Louis XVI" ("The Life of Madame Elisabeth, Sister of Louis XVI). I haven't read this one (although I now endeavour to) but unfortunately, it's in French as well.