This paper explores downlink Cooperative Rate-Splitting Multiple Access (C-RSMA) in a multi-cell wireless network with the assistance of Joint-Transmission Coordinated Multipoint (JT-CoMP). In this network, each cell consists of a base station (BS) equipped with multiple antennas, one or more cell-center users (CCU), and multiple cell-edge users (CEU) located at the edge of the cells. Through JT-CoMP, all the BSs collaborate to simultaneously transmit the data to all the users including the CCUs and CEUs. To enhance the signal quality for the CEUs, CCUs relay the common stream to the CEUs by operating in either half-duplex (HD) or full-duplex (FD) decode-and-forward (DF) relaying mode. In this setup, we aim to jointly optimize the beamforming vectors at the BS, the allocation of common stream rates, the transmit power at relaying users, i.e., CCUs, and the time slot fraction, aiming to maximize the minimum achievable data rate. However, the formulated optimization problem is non-convex and is challenging to solve directly. To address this challenge, we employ change-of-variables, first-order Taylor approximations, and a low-complexity algorithm based on Successive Convex Approximation (SCA). We demonstrate through simulation results the efficacy of the proposed scheme, in terms of average achievable data rate, and we compare its performance to that of four baseline schemes, including HD/FD cooperative non-orthogonal multiple access (C-NOMA), NOMA, and RSMA without user cooperation. The results show that the proposed FD C-RSMA can achieve 25% over FD C-NOMA and the proposed HD C-RSMA can achieve 19% over HD C-NOMA respectively, when the BS transmit power is 20 dBm.