Boolean modifiers have three modes:
Which are pretty self-explanatory. Intersect only leaves the part of the mesh which is intersecting with the other, Union unites the two meshes and Difference only leaves the difference between them.
We're looking at using the "Difference" option here. The issue with this is that it subtracts volumes - this means that if you subtract a cube from another cube, you get something like this:
However if I use the "difference" option with a plane instead of a second cube I get this:
But that's still a cube! So what happened here? Well, let's take a look at it in edit mode, shall we?
There is our answer. It did subtract the plane! However a plane doesn't have any thickness to it, so it just cut our cube in half!
This is the issue you're facing at the moment with your walls. The inner and the outer wall both get subtracted, however they are both planes. This means that you get your floor cut properly, but it doesn't actually subtract the part you don't want to have. So to fix this you have to apply the modifier (I had to apply it as well, to show you what it did). Once you have done that you can go into edit mode and hover over the part you don't want. Blender has a nifty feature that allows you to select loose parts of a mesh, so hit "L" to select them. If you, in doing this, also select the part you want then that means that you haven't completely seperated them and they're still connected somehow.
This has one disadvantage tho. Booleans in general are great for non-destructive modeling, meaning that you can add them and never apply them. This allows you to keep your original mesh intact. You just hide all the things you subtract to get them out of the view.
This technique doesn't allow you to do that, unfortunately.
If you want to do it without booleans, here's an idea I have: Go into edit mode on one of the walls. Select only the lowest vertecies. Hit Shift + D to duplicated them, then hit P to put them into a new mesh (Press P -> "From Selection"). Enter edit mode on the new mesh, select all vertecies, and scale them down or up intul you meet the other wall.