A process for recovering non-ferrous metals, in particular copper, nickel and cobalt, from metallurgical residues containing these non-ferrous metals at an oxidation state of greater than or equal to zero, in an alternating current type plasma arc electric furnace comprising a plurality of electrodes, containing a liquid copper heel covered by a fluid slag comprising at least one fusion-reduction phase, comprising charging of metallurgical residues comprising the non-ferrous metals onto the heel contained in the plasma arc electric furnace, fusion of the metallurgical residues in the fluid slag or at the slag-metal bath interface, reduction of at least the non-ferrous metals to oxidation state zero, and intense stirring of the copper heel by injection of inert gas, preferably nitrogen and/or argon, so as to avoid crust formation and to accelerate the reduction reaction and to cause the copper-miscible non-ferrous metals to pass into the copper heel.