It's possible to represent second derivatives in a form, such as assemble(div(grad(f))*dx). I assume this is true in FEniCS as well as Firedrake, because this is just UFL/FFC/FIAT functionality. This would produce the sum (over cells) of the Laplacian of f on each cell.
However, like FEniCS, none of our function spaces have more than C^0 continuity. That is, the functions are at most continuous, but won't have continuous derivatives. It's likely that you won't want to use second derivatives of C^0 functions in a practical discretisation (though I'm sure there are methods that *do* do this).