The present work reports on high-precision measurements of forward-angle fragmentation differential cross sections for the [12]C +[12] C reaction at 62 MeV/nucleon using the FAZIA array. Angular distributions for fragments from Z = 1 to 6 were extracted in the range 2 <= theta_lab <= 8 degrees. Particle identification was achieved by combining the Delta E - E technique with Pulse Shape Analysis, and precise energy calibrations were performed. The results show that for heavier fragments, the angular distributions are better described by the Van Bibber formulation than by the Goldhaber model, consistent with the dominance of a wide component from dissipative processes in the measured angular range. Notably, alpha particles exhibit an anomalously narrow angular distribution, likely originating from the intrinsic cluster structure of [12]C. Comparisons with existing data at the same incident energy show very good agreement, with a more complete set of species reported here, while a kinematic scaling is proposed to compare our data with previous experimental data at 50 and 95 MeV/nucleon.