The correlators of two-dimensional rational conformal field theories that are obtained in the TFT construction of Fuchs, Runkel and Schweigert are shown to be invariant under the action of the relative modular group and to obey bulk and boundary factorisation constraints. We present results both for conformal field theories defined on oriented surfaces and for theories defined on unoriented surfaces. In the latter case, in particular the so-called cross cap constraint is included.