Why doesn't this V-Brake fit my frame? As part of a bike rebuild I'm working on, I replaced the old cantilever brakes with new Shimano V-brakes.

The problem is that the new front brake doesn't seem to fit with the wheel.
The rim walls are relatively low compared to brake pads and the brake pads can't go any lower. In fact where they sit now is also problematic because it's always touching the rim walls.

Attached is a photo of the bike. 

Update: It's a 28/700c Villiger frame. I double checked it.
Your frame is designed for the type of cantilever brake you already had, which has pads closer to the pivot than modern brakes. Unfortunately it looks like you are stuck with your old brakes.

The old brakes can be improved with new cables and pads and lubricating the pivots.