General:
* Rural poem
* Country poem
* Pastoral poem (especially if it focuses on idealized countryside life)
* Nature poem (if it highlights the natural world)
* Folk poem (if it draws on oral traditions or vernacular language)
More specific:
* Farm poem
* Harvest poem
* Mountain poem
* Wilderness poem
* Backwoods poem
You could also use terms that describe the style or tone of the poem:
* Simple
* Down-to-earth
* Grounded
* Honest
* Authentic
Ultimately, the best way to describe a rustic poem is to use terms that accurately reflect its specific subject matter, style, and tone.