Old analog television sequences suffer from a number of degradations. Some of them can be modeled through convolution with a kernel and an additive noise term. In this work, we propose a new blind deconvolution algorithm for the restoration of such sequences based on a variational formulation of the problem. Our method accounts for motion between frames, while enforcing some level of temporal continuity through the use of a novel penalty function involving optical flow operators, in addition to an edge-preserving regularization. The optimization process is performed by a proximal alternating minimization scheme benefiting from theoretical convergence guarantees. Simulation results on synthetic and real video sequences confirm the effectiveness of our method.