The best replacement for fable is folktale.

The best alternatives to fable are rated as following:
★★★★★  folktale
★★★★  parable
★★★★  fairy tale
★★  fable the lost chapters
★★  myth
★★  oblivion
★  elder scrolls
★  fable lost chapters
★  allegory
★  skyrim
★  morrowind
★  legend
★  jade empire
★  lost chapters
  assassins creed
  fairytale
  dragon age
  witcher
  pabula short story
  fable tlc
  fable anniversary
  adventure quest
  kingdoms of amalur
  tall tale
  folklore

Your alternative for fable is not listed? Suggest!
Speaking about fable, one probably shouldn't forget about morals.

Other search terms related to fable and their ratings are:
★★★★★ morals
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