Stone, concrete, or masonry foundations don't need to dry, not at all, in any direction, for any reason. There are examples of bridge foundations made of stone & concrete that have survived millenia of submersion and are still functioning fine. It's the wood in contact with foundations that needs to stay dry.
Stone foundations also have lower capillary draw than concrete, and even if the footing is in water, if there's at least foot or so of above grade exposure (and reasonable roof overhangs to limit splash-back wetting), the foundation sill is pretty safe. But if there's any question at all, jacking up the house a hair and slipping the membrane between the foundation and foundation sill isn't as scary a process as it might seem.
To put down a finish floor, even with French drains you would need both a ground vapor barrier (10mil poly, or membrane) as well as rigid EPS or XPS insulation between the cool concrete and the sub-floor. The amount of insulation required varies with local subsoil temps and climate, and whether the space will be mechanically dehumidfied. Got a zip code?