A few random thoughts and questions.
1 It seems unlikely that the true ground water table is that high in Ohio. I would guess there is a shallow non permiable layer of clay in that area causing the surface water. If that is the case, digging through the clay layer may drain the area, good or bad.
2 How big is the wet area?
3 A pond can be easily dug with an excavator in a wet area, it doesnt matter if it fills as it is being dug.
4 If you are raising the yard, why bother with the french drain? Can you just build a gentle slope for drainage?
5 you may want to check with Local NRCS office or website and look at the soil survey of your area, it is not exact but may be a start in understanding what you are dealing with.
