Why don't you want to change the spelling ?
If you like the name Alexander, I don't think that changing two letters would change anything for your son
even more since most of the names that have the same spelling in French and English don't have the same pronunciation.
To tell the truth, it's something I hadn't ever thought about (we have Greek, French and English here as I'm Greek-Belgian and my husband American). When my husband came up with the name Nicholas and, yes, I thought "oh, that's nice, that's a name who exists and sounds good to me in the three languages" but it's not the reason why I accepted it. (by the way..; he decided a few months ago that if the baby is a boy, it will be spelled Nikolas to look more Greek
) I picked the girl's name, Joyce, and I have no idea how that will be pronounced in Greek but, well, I'm sure we'll find a way to write it
You know, my name is Electra in French ans Ilektra in Greek, having different pronunciations of my name never bothered me
(and now I'm really curious to hear how you pronounce Xavier in English :-D )