You could bury it an inch or so and lay in a run of patio blocks along the bottom of the fence outside (makes a nice mowing strip).
Or you could lay the wire out (away from the protected area) along the ground 8-12 inches.
Actually, I have the pavers where lawn meets the veggie garden fence and wirealong the ground where there are (unprotected) flower beds.
jumping >over and into the garden?
18-24 inches should suffice.
(My fence is 48" tall with 18" of 1 inch hex net along the bottom and two electric strands at the top, protected on the bottom as I mentioned. Seems to work.)
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