  Campana introduced a notion of Campana rational connectedness for Campana
orbifolds. Given a Campana fibration over a complex curve, we prove that a
version of weak approximation for Campana sections holds at places of good
reduction when the general fiber satisfies a slightly stronger version of
Campana rational connectedness. Campana also conjectured that any Fano orbifold
is Campana rationally connected; we verify a stronger statement for toric
Campana orbifolds. A key tool in our study is log geometry and moduli stacks of
stable log maps.
