Recently developed single-root multireference Brillouin-Wi,oner coupled-cluster (MR BWCC) theory, which deals with one state at a time while employing a multiconfigurational reference wave function, is applied to the ground state of the Fr! molecule using a two-determinant reference space at the level of the CCSD approximation. The method represents a brand-new coupled-cluster (CC) approach to quasidegenerate problems which combines merits of two theories : the single-reference CC method in a nondegenerate case and the Hilbert space MR CC method in quasidegenerate case. The method is able to switch itself from a nondegenerate to a fully degenerate case in a continuous manner, providing thus smooth potential energy surfaces. Moreover, in contrast to the Hilbert space MR CC approaches, it does not contain the so-called coupling terms and completely reduces to the standard single-reference CC method in a highly nondegenerate region. Using a [4s, 3p, 1d] and [4s, 3p, 2d, 1f] basis sets, the calculated potential energy curves are smooth, dissociate correctly and the results are compared with other available multireference techniques as well as experiment.