Direct acceleration of electrons in a coherent, intense light field is revealed by a remarkable increase of the electron number in the MeV energy range. Laser irradiation of thin polymer foils with a peak intensity of ∼1×1020 W/cm2 releases electron bunches along the laser propagation direction that are postaccelerated in the partly transmitted laser field. They are decoupled from the laser field at high kinetic energies, when a second foil target at an appropriate distance prevents their subsequent deceleration in the declining laser field. The scheme is established with laser pulses of high temporal contrast (1010 peak to background ratio) and two ultrathin polymer foils at a distance of 500 μm. 2D particle in cell simulations and an analytical model confirm a significant change of the electron spectral distribution due to the double foil setup, which leads to an amplification of about 3 times of the electron number around a peak at 1 MeV electron energy. The result verifies a theoretical concept of direct electron bunch acceleration in a laser field that is scalable to extreme acceleration potential gradients. This method can be used to enhance the density and energy spread of electron bunches injected into postaccelerator stages of laser driven radiation sources.