Way back on early drafts of "Unofficial Chrono Trigger 2," I had assumed that Elaine and Fritz were fiancees, and so wrote them as married. However, in my recent game of Chrono Trigger for the DS, I can't find any cues that would indicate that they're betrothed: in fact, since the Truce item store is family-owned, they may be siblings.
Can anyone provide any concrete evidence for one or the other interpretation, be it from the Woolsey translation, the on-site Retranslation, or the DS translation?