I’d say it like [name_u]Ash[/name_u], but like ze-[name_u]LEE[/name_u], with the stress on the last syllable. But if you wrote it Zélie, I’d say zay-[name_u]LEE[/name_u]. I wouldn’t expect it as a nickname for [name_f]Elizabeth[/name_f], but it’s cute and could work,and maybe the unexpectedness is part of the appeal.
I pronounce it zay-lee, and it’s a quirky nickname for [name_f]Elizabeth[/name_f]. I think it works.