Gender-independent replacement for “fiancée” and “fiancé”
For formal writing, betrothed would be my number one choice. But, as Lunatik already gave that answer, I'll provide some more: spouse-to-be (instead of the gender-specific wife-to-be and husband-to-be), future spouse, prospective spouse, intended (date and informal).
Of course, it's much easier to refer to use adjectives and refer to the couple as a whole, if you can rewrite it in this way. This opens the door to: engaged, affianced, pledged in marriage, etc.
"Betrothed" can be used as a noun, but I admit it does sound a bit stuffy.