Floor joists typically 'stagger' half way onto a central bearing beam.
Depending on the span, species of lumber, whether they are true 2"x8" joists, and their spacing on center...your current joists can be entirely acceptable for your floor load needs.
Likewise, if your 'front' and 'back' walls are not load bearing, it shouldn't much matter if there is any daylight at the point they join the foundation since there are no loads being transferred here.
Please describe in detail what you are seeing. For the moment I see no problem.
In a house this old, substandard carpentry would have shown up before this. It is more likely that current settling in is due to rot or insect danage softening the wood.
The house is about 26' deep and the span between the front wall, and the center beam, and the center beam and the back wall is about 13'
Rot and insects are not a factor, I am thinking that its a combination of not enough support, and poor soil under the house.