Consider weak approximation for 0-cycles on a smooth proper variety defined over a number field, it is conjectured to be controlled by the Brauer group of the variety. Let X be a Châtelet surface or a smooth compactification of a homogeneous space of a connected linear algebraic group with connected stabilizer. Let Y be a rationally connected variety. We prove that weak approximation for 0-cycles on the product X × Y is controlled by its Brauer group if it is the case for Y after every finite extension of the base field. We do not suppose the existence of 0-cycles of degree 1 neither on X nor on Y.