Plasma wakefield acceleration (PWFA) is a novel acceleration technique with promising prospects for both particle colliders and light sources. However, PWFA research has so far been limited to a few large-scale accelerator facilities worldwide. Here, we present first results on plasma wakefield generation using electron beams accelerated with a 100-TW-class Ti:sapphire laser. Because of their ultrashort duration and high charge density, the laser-accelerated electron bunches are suitable to drive plasma waves at electron densities in the order of 1019 cm-3. We capture the beam-induced plasma dynamics with femtosecond resolution using few-cycle optical probing and, in addition to the plasma wave itself, we observe a distinctive transverse i...