If the aircraft says Cat 3 single then plan for Cat 3 A approach. The reason you don't get an ECAM caution is because there's no associated ECAM message or actions for the specific failure - as others have said it is often down to an ADR disagree, and one of the reasons we review the status page before starting an approach.
CFDS will give you a rough idea in flight if you're curious with more detailed reporting on the ground.