OpenGL Framebuffer with multiple Depthbuffers inside
FBOs can only use a single depth image, but that image can be layered. Broadly speaking, VR multi-eye rendering ought to be done through layered FBO images for both the color and depth buffers.
The problem with your code is that you can't use glFramebufferTexture3D to attach a layered image. You must use glFramebufferTexture.
Also, you need to use layers for the color image as well.