I'm excited about the progress being made in the FEM module. Of the free FEA options available, I think that Calculix, Elmer, and Code-Aster are all great FEA programs to hook Freecad up to.
Out of those options, Calculix has a very straightforward input file syntax, and it is mature as TT-RS said.
I was also frustrated with the lack of easy to use FEA freeware, so I wrote a python library to wrap around Calculix:
It allows the user to build, mesh, solve, and post-process 2D Calculix models (plane stress, plane strain, and axisymmetric) from within Python.
Perhaps my code can provide some insight into interfacing with the Gmsh mesher, which it uses.
Gmsh can produce quads, tris, tets, hex, etc. elements.
Pycalculix is good for 2D trade studies, but in the long term, users need easy to use FEA freeware built into a CAD program, and I'm happy to see that Freecad is making progress in this area.