How to protect soil up against new wood fence base
Having dirt touching the fence will increase the chance that the bottoms of your rails/pickets will rot. This doesn't necessarily mean your whole fence will rot; only the parts exposed to heavy moisture are at risk. Maybe you're OK with having a bit of rot on the hard-to-see part of the fence after a few years; how bad it is really depends on the wood, how wet the climate is where you are, how much sun that area gets, etc.

If you want to protect the fence, I see three options:


Cut the bottom end of the pickets so it's no longer touching the dirt. If needed, treat the cut to improve rot resistance (may not be needed on natural redwood cedar, but you said it was pre-treated, so any cut surfaces should be treated in the same way).
Add stone/gravel to provide free-draining surroundings as you suggest. (I wouldn't recommend plastic as it's likely to just trap moisture against the fence and accelerate rot.)
Remove some dirt near the fence (may be too much work, or against your landscape design goals).