PARIS—On the night Paris Saint-Germain qualified for the Champions League final and put itself 90 minutes from European glory, the three biggest signings in the club’s history were nowhere near the French capital.

Lionel Messi, Kylian Mbappé, and Neymar, who’d all been signed for this very purpose, were long gone, scattered to Spain, Brazil, and South Florida. The trio of planetary superstars were supposed to be the ones to launch PSG into the stratosphere and bring home a first Champions League trophy.