OK, the moment I saw
Cateline, I thought cat-a-LEEN (like the French way you mentioned, but I hadn't read that far yet), closer to like
Catalin than
Caitlin. I wouldn't pronounce it
Caitlin at all, though maybe if you dropped the E off the end. You'd probably get lots of people saying Kate-leen or Kate-line.
I don't mind
Caitlin, but it is really common and I'm not too keen on the name
Lyn, anyway. I know at least three with these spellings:
Caitlin,
Caitlyn and Kaytlyn. The last one detests her name and goes by Kayt (ie
Kate). My favourite spelling is
Caitlin.