There is some discussion of this in previous threads here and [here] (https://www.reddit.com/r/AskHistorians/comments/3h3o8t/what_happened_to_the_ww1_trenches_when_the_war/)

This comment from /u/TheWellSpokenMan is a good summary.

Graves Registration, Ordnance Disposal and salvage units gradually swept across fought-over areas, collecting bodies, munitions and scrap, a process which took years and still goes on in a limited sense. This snippet of airship footage from 1919 gives a tiny sense of the scale of destruction, and shows trench lines still untouched (around 1:40).

Then depending on the value of the land, residents might return, restore it and resume use (in the case of good agricultural land, for example). Some areas were preserved for memorial reasons. Other areas were simply abandoned and left to nature, either because of low value or due to official Zone Rouge decree because the soil is so toxic with gas, heavy metals and other pollutants, categorised immediately after the war as:

"Completely devastated. Damage to properties: 100%. Damage to Agriculture: 100%. Impossible to clean. Human life impossible"