I read some online reviews for this, and I was dismayed by how many people didn't seem to enjoy it. Since The Moon and the Sun is one of my all time favorites I feel the need to even up the reviews somewhat. I will not overview the plot, so many have done it much better than I could, but I will explain why it is a personal favorite.
There are some quibbles about which genre this novel belongs in: Science Fiction, Historical Fiction, Romance, Fantasy etc. The answer is simply that it belongs to all of them. There are so many elements to the story that it borrows from many genres; it involves fantastical mermaids that are studied scientifically by a Jesuit priest in the royal court of king Louis XIV's Versailles. See what I mean?
The Historical side of the novel is very well researched, and the detail of the fashion, etiquette and intrigue take up a good amount of the page space. Not only is Louis XIV realized credibly, but so are real life members of his court all brought to life by vivid and extreme detail. Some may find this tedious, but personally, these are the exact kind of things I enjoy in historical fiction.
This detail of the time is not limited to dress and setting, it extends to characters also. The reader is made aware of exactly who everyone is, where they come from, what their standing in court is and also why they do the things they do. This does take time, so the beginning of the novel is bogged down with the machinations of the court and a great deal of dialogue between the characters, but again, this is precisely the kind of unhurried and meticulous characterization that I enjoy.
While all the character's follow obvious archetypes, they are not one dimensional. Marie may be the Naive Beauty and her brother may be the Stoic and Moral Scholar, but they are both so much more than that. Marie is a woman of ideas who struggles with the belief of the time that women are not supposed to even have ideas. Her brother is also a man of ideas, but struggles with balancing the morals of his order and the strictures of society. In the court they are surrounded by the greedy, the immoral, the disillusioned and the spiteful and lusty lot that make up the Royal Court. Every character, even the minor ones, have some personal struggle.
There are some hokey or "cheesy" moments, and these are what appeal to the romantics and the dreamers, but I think these light hearted and fanciful moments are needed to balance out some equally morbid and dark parts of the novel. There is a love story but there is also a good deal of hate, prejudice, misogyny, deceit and plain viciousness. This is the main reason I enjoy the novel so much, that many of the characters and their issues bring up interesting ideas about ethics.
It really isn't that difficult to figure out where the plot is headed, but following the predictable plot is no less enjoyable simply because you know where its going. The story as a whole is represented by the mermaid itself, not a lovely siren but an ugly humanoid fish, a metaphorical symbol of all the characters in the court: creatures bound by the beliefs and expectations of others, forced to hide the things that truly make them happy.