High-T_c cuprate superconductors are known to exhibit multiple charge- and spin-ordered phases, whose interplay with superconductivity is expected to provide crucial insights on understanding high-T_c superconductivity. Stripe order that is seen in La-based cuprates is the representative case that exhibits strong competition with the superconductivity, where charge and spin are align in a form of stripes in CuO₂ plane. To investigate the microscopic interplay between stripe order and superconductivity, we performed optical pump-terahertz probe spectroscopy along c-axis of stripe-ordered cuprate La_1.6-xNd_0.4Sr_xCuO₄ (x = 0.12) above T_c. We found a sharp plasma edge appearing in the reflectivity spectrum just after photo-excitation, followed by redshift within a few ps. This plasma edge was observed below charge-ordering temperature T_CO = 69 K. Below spin-ordering temperature T_SO = 55 K, a long-lived reflectivity enhancement was identified. Based on these experimental results, we discuss the interplay between the charge/stripe order and the superconductivity.