An optical frequency domain reflectometry (OFDR) shape sensor was demonstrated based on a femtosecond-laser-inscribed weak fiber Bragg grating (WFBG) array in a multicore fiber (MCF). A WFBG array consisting of 60 identical WFBGs was successfully inscribed in each core along a 60 cm long MCF using the femtosecond-laser point-by-point technology, where the length and space of each WFBG were 2 and 8 mm, respectively. The strain distribution of each core in two-dimensional (2D) and three-dimensional (3D) shape sensing was successfully demodulated using the traditional cross correlation algorithm, attributed to the accurate localization of each WFBG. The minimum reconstruction error per unit length of the 2D and 3D shape sensors has been improved to 1.08% and 1.07%, respectively, using the apparent curvature vector method based on the Bishop frame.