Judge Judy, who sees quite a few ex-fiancées in her courtroom,
always sides with the would-be groom regarding engagement rings. Her belief, and mine, is that the engagement ring is not a gift in the conventional sense, but one that is specifically linked to the engagement and upcoming wedding. If the engagement is off, he gets the ring back.
A stickier situation would be what to do if a couple did get married, but broke up shortly after, say within six months. The engagement, and its ring, are fresh in mind.
See also: the landmark case of
Burrito v. Sandwich.