I say cat-uh-LEEN (similar to the French, but not quite), but if I was a reader I'd either settle on Kate-leen or Kate-line. The problem with character name pronunciation is that really the reader decides how they're going to say it, and often don't realize they're wrong. I do like
Caitlin, but not spelt
Cateline, and I think KATE-leen would be better spelt as Caitleen or something.
I like
Caitlin a lot. I know a
Caitlin, a
Kaitlyn, a
Caitlyn, and a
Katelyn. I've also seen
Katlyn pronounced that way which I really don't like.
Katelyn is my favorite, mostly because I'd want to use
Kate as a nickname and that way it's more intuitive.