Is there a contact model in FEniCS for two imported physical volumes?

FEniCs is used for both research and industry. See for instance: https://arxiv.org/pdf/1804.10060.pdf
on large scale physical problems.
Im myself working on contact modell for FEniCS using multi-point constraints. I can let you know Once this is published.

For your case, it is easy to Connect the meshes,
Using boolean fragments in Gmsh. See:
Pygmsh Tutorial? for a simple use case.

If you Connect the meshes, the interface condition between the two objects will be that displacement on one side is equal to the displacement on the other side. (Both normal and tangential components)

Forces on surface is the same as applying traction on the top surface. This can be done using Measures and subdomains, see for instance:
Transitioning from mesh.xml to mesh.xdmf, from dolfin-convert to meshio for a minimal code using a restricted surface measure.

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