A process for manufacturing composite sheets includes steps of: continuously depositing a web of yarns, in the form of a mat of continuous yarns, a woven, a knit or an assembly of continuous non-interlaced yarns on a moving substrate; depositing a powder of an organic material capable of forming a coating layer under the action of heat on at least one side of said web; heating the web coated with the powder to a temperature sufficient to melt the powder; compressing and cooling the web so as to form a composite strip; and cutting the strip in the form of sheets or winding the strip up on a rotating support.