The interaction of a laser with an over-critical foam of high-density contrast is investigated numerically using the hydrodynamic code FLASH to better understand the effect of the foam structure on the propagation of shocks. Two representative cases are compared to the case of a homogeneous material with a density equal to the foam average density. In the first case, the whole foam structure is directly exposed to the laser. We found that a shock wave is generated and has similar properties to those of the homogeneous case. In the second case, the laser penetration into the foam is blocked by an overcritical plasma layer that acts as a laser-driven piston. Thus, the laser-driven shock wave homogenizes the solid structural elements in the foam. The propagation speed and internal structure of the transient zone are different, and a significant amount of energy is stored in turbulent kinetic energy. The properties of turbulence are also discussed.