There would be less firearm-related violence but a significant increase in murders. It is generally assumed that one is safe within a gun-free zone. Observation of media reports suggests that most reported massacres occur in gun-free zones. It may be that massacres in schools and other places, may be a direct result of anti-gun legislation. The law, in itself, does not deter violence.
Violence is deterred only if there is a physical deterrence to that violence.
There are various examples around the World where massacres have been stopped by legitimately armed members of the public when law enforcement personnel have not been present or have been unwilling to become involved. The concept of searching for illegal weapons is good, but the concept of gun-free zones instils a belief that the area cannot be subject to illegal violence. Gun-free zones deny the Right to Life and Freedom from violence should an attack occur. Legislated gun-free zones may therefore result in an increase in massacres, rather than the aspired for reduction in murders. A better solution may be 'Gun Control Zones'.