This has a mix of Japanese and European stories, graded by primary school level.
http://hukumusume.com/douwa/0_6/index.html
There are some stories such as The Emperors New Clothes in the supplied library of iBunkoS on the iPhone.
As well as some Beatrix Potter titles.
http://itunes.apple.com/us/app/ibunkos/id418102178?mt=8
http://nagisaworks.com/ibunkos/index.html
You might be able to find some on
http://www.aozora.gr.jp/
You can search for Hans Christian Anderson or Grimm,( and maybe an English title but I haven't tried.)
I'd say they need a much higher reading level though.