Does I need both targets to be able to play Star-Crossed?

Yes, you need both targets to be able to play Star-Crossed.

According to Rule 355.10, a game object mentioned in the text of a spell is a target unless it falls under specific exceptions. Because Star-Crossed instructs you to return "a friendly unit and an enemy unit," both are required targets.

Furthermore, as established by RiftJudge FAQ 1462 (regarding Back to Back), spells that require multiple targets without "up to" language require all targets to be present and valid to be played. You cannot cast Star-Crossed if you do not have both a valid friendly unit and a valid enemy unit to target.