This study considers the problem of direction-of-arrival (DOA) and polarisation estimation based on a single six-component electromagnetic vector-sensor. A regularised parallel factor analysis (PARAFAC) model that fuses both second- and fourth-order statistics of the sensor signal is established within the regularised framework. The steering vectors can be uniquely identified by exploiting the link between this trilinear model and PARAFAC, from which unambiguous estimation of 2-D DOAs and polarisation states can be further obtained. The proposed method combines the nice variance property of second-order statistics and the intrinsic multi-invariance structure of fourth-order cumulant (FOC) in a tensorial manner, and offers better performance than regularised estimation of signal parameters via rotational invariance techniques and FOC-based PARAFAC in the presence of noise and finite data length. Simulations are provided to illustrate the performance of the proposed method.