We focus on the optical signal-to-noise ratio (OSNR)-aware optical path (lightpath) planning problem in spectrally and spatially flexible optical networks (SS-FONs) connected using weakly coupled multi-core fibers (MCFs) in which distance-adaptive and super-channel transmission is realized using multiple modulation formats. In the SS-FON considered, the quality of transmission (QoT) of optical signals is degraded due to the inter-core crosstalk (XT) effect occurring in MCFs. To account for the XT impairment when planning lightpath connections, we make use of a reliable QoT model based on the OSNR estimation, in which the XT impairment is integrated with other physical-layer impairments. To model the lightpath planning optimization problem, we develop a novel mixed-integer programming (MIP) formulation that incorporates the OSNR model. In addition, we propose an efficient heuristic method that is capable of solving larger instances of the optimization problem considered. The results of numerical experiments indicate the low scalability of the MIP method due to the presence of XT and high effectiveness of the heuristic method. The analysis of three different network topologies and two types of MCFs shows a high impact of XT on network performance and limited performance gains from the presence of the central core in a 7-core MCF.