Can you activate Star-Crossed if only one player controls units?

No. You cannot play Star-Crossed if only one player controls units on the board.

The spell reads "Return a friendly unit and an enemy unit to their owners' hands." Both are mandatory targets — there is no "up to" language. You need a friendly unit and an enemy unit on the board at the time you announce the spell and place it on the chain. If only one player has units, one side of the targeting requirement can't be met, and the spell can't be played.