It's difficult to tell from the photos, but it appears to be that the stones were laid on top of the soil and not constructed as an actual wall. Unless the wall is hiding behind the fence.
How long ago was the fence installed? Have you removed sections of fence to inspect what is behind it?
I have some experience building walls; there is a lot about a stone wall that you cannot see. The most important parts are in the base design, the angles required for the wall to be self-supporting (to rest), the larger stones placed at intervals to support all of the smaller stones, the all important backfill material.
This does not seem like an easy fix. Something as large as what is in the photos, plus the fact that it is on a grade, seems more likely to require a professional.
