I've underplanted various things under existing apple trees (after first sheet mulching with cardboard and a good layer of woodchips to smother the existing grass/weeds). Plants that seem to have worked best and stayed around longest:
1 ) Groundcover strawberries (which flower but don't really fruit) from Oikos, variety "Kelly's Blanket"
2 ) Ostrich Ferns
3 ) Lower-growing Mints
4 ) Clovers (tend to only persist in the sunnier spots)
5 ) Comfrey (seems pretty shade tolerant, though it won't grow as well in full shade)
6 ) Lunaria aka "Honesty / Money Plant", Dame's Rocket and other Spring ephemerals like Daffodils, Dandelions and Ramps
7 ) Sweet Woodruff (aggressive spreader for shade, though not all that useful)
8 ) Wood Poppy (aka Celandine Poppy), early flowering plant, aggressive re-seeder
9 ) Solomon's Seal (good "asparagus" crop for shade, though may grow taller than you'd like, and deer nearly killed my patch this year)
10 ) Groundnut (I'd intended these to grow up into the trees, but they have a mind of their own and sprawl wherever they want to)
I usually end up throwing some inexpensive seeds of various clovers, daikon radishes, turnips, brassicas and other "forage" crops around, and a few will take root and grow, but since it's fairly shady, they usually don't persist or thrive.
One hot tip: Nettles are a wonderful plant to grow on the edge of a property, but best NOT to plant them under fruit trees, turns into a scratchy maintenance/harvest problem.