Shade is actually perfect for a leafy green garden it make the vegetables produce bigger and softer leaves to catch the max amount of sunlight. They also stay softer for longer and don't bolt and get bitter as quickly. And because you aren't trying to capture extra sunlight to make pounds and pounds of sugary fruit, you don't need that much sunlight.
Shade Tolerant Plant List
* Leafy Greens (lettuce family, spinach family, cabbage family)
* Herbs (onion family, mint/thyme family)
* raspberry/blackberry/strawberry
* goumi
* artic kiwi
* pawpaw
* juneberry (but I think they get infected with cedar pine rust too much to be worth it)
* cornellian cherry (this has actually done well for me, the plants are a tiny bit too tall for me)
* Mushroom (they love the shade and moisture, you can do oyster and winecap with minimal prep, chicken of the woods/etc if you want to be more iinvolved)
* Bee Hive (get two flow bee hive from amazon.com, they don't require any tools to harvest just spin a knob and honey flows out)
* Egg (get 6 or so egg laying chicken, and a coop, with a woodchip floor and you can throw waste food (home/supermarket/etc) to grow worms/insects for them.
All that said what exactly is a forest garden. I know that this will differ depending on who you ask. For me a food forest is actually most similar to oak savanna/prairie/silvo-pasture. With lots of spacing between plants vs a dark forest floor of a regular forest.