The weak-localization phenomenon for two-dimensional (2D) electronic systems is invoked to explain the negative magnetoresistance as well as the low-temperature dependence of the resistivity of pyrocarbon samples heat treated between 2000 and 2600 C. The 2D character is found to originate from the random stacking of the graphene layers (turbostratic structure) characteristic of pregraphitic carbon materials. For a heat-treatment temperature (HTT) lower than 2200 C, x-ray analysis reveals that the structure is almost turbostratic, while the material exhibits a pronounced negative magnetoresistance. For higher HTT, 3D order typical of crystalline graphite increases, leading to a 2D-to-3D crossover and to a vanishing negative magnetoresistance.