In the context of the French Laser-Mégajoule fusion-research programme, a direct-drive target design is developed. It is based on the use of a CH-foam ablator filled with cryogenic deuterium–tritium. One-dimensional optimization leads to a potential gain of 60 with a 1.5 MJ laser. The hydrodynamic stability of the implosion is investigated at the ablation front and the hot-spot surface by means of modelling and two-dimensional simulations. The effect of irradiation non-uniformities on low-mode (time-dependent) implosion asymmetries is studied by two-dimensional hydrodynamics simulations with three-dimensional laser-light raytracing. The effect of beam focal shapes on hot spot low-mode asymmetries is also addressed.