BRUSSELS—Belgian police had numerous chances to unmask the Islamic State terror cell that later carried out the Paris and Brussels attacks, according to a confidential report prepared for Belgium’s Parliament. They muffed every one.

In early 2015, Brussels police stopped a car driven by Brahim Abdeslam, later one of the Paris attackers, and arrested him for drug possession. At the time, Brahim was on a terror watch list. He carried a booklet about “parental consent for the Jihad.” Police found a USB thumb drive hidden behind...