Madeline (pronounced mad-er-lin, like Catherine) is the trad English spelling (cf Keats) and more common in Ireland also.
Madeleine is the Fr spelling.
The Fr one is probably more common in the UK now, but we've come across both.
You can have pronounciation probs either way, tbh -- if you go for Madeleine people may say it mad-er-layne to rhyme with Elaine.
Otoh, if you go for Madeline, some people may pronounce it mad-er-lyne to rhyme with Caroline. And this is the pronunciation used in the film of the book -- maybe that's the US pronunciation?
I think the potential for mispronunciation is because the -ine spelling can be said in various ways, cf Caroline, Catherine, Josephine. You have to decide which mispronunciation would annoy you least. It's a pretty minor annoyance in the great scheme of things. 