If the soil is not compacted, I would not attempt to disturb the soil. Doing so will expose weed seeds and disrupt the natural structure of the soil. Oddly, enough you run the risk of compacting the soil. There are two ways this could happen: the natural structure of the soil is stable, by rotavating it you make it unstable and it will soon collapse back ...
Bearded Iris (Iris germanica)
Bee Balm (Monarda)
Butterfly Bush (Buddleia davidii)
Echinacea (Echinacea purpurea)
all excellent plants in clay soil
As for grass "Tall Fescue" grows best. But if you're looking to break it up.
Break up your clay soil by digging/mixing a ...
I'm not sure about in clay specifically, but you might try reeds, rushes, Job's tears, mint, irish moss, cranberries, wild rice, stinging nettle, some kinds of bamboo, wild irises (not the domestic ones), watercress, water chestnuts, asparagus, and stuff like that.
Here's a link that supports some of those.
I'm currently growing Iceberg Lettuce in forest soil, mixed with wood ash and decomposed tree log wich easily turns like dirt. The soil had alot of organic matter, specially roots.
Still growing great!
I am a big fan of drainage around the house but it's a challenge as water will go where it wants to go.
Yes, if you backfill with gravel and top with more landscape fabric to keep out the soil then turf it will drain better for the area on top of the French drain.
I suggest using a level to see where the slope is. Laser levels are readily available and if ...