The industrial waste generated in the extraction of carrageenan from red seaweed, Eucheuma spinosum, was tested in this study to produce fermentable sugars that could be used for the production of high‐value‐bioproducts with a biorefinery approach. A sequential process was used: thermochemical pretreatment with HCl and enzymatic hydrolysis. Hydrogen chloride concentrations in the range from 0 mol L−1 to 0.5 mol L−1 and pretreatment times from 15 to 100 min were assayed. The best conditions found for pretreatment were HCl 0.3 mol L−1 for 60 min, leading to reducing sugar concentrations of 21.4 g L−1 (274 mg of reducing sugars per gram of algal residue). The hydrolysates coming from the sequential process under the pretreatment conditions of HCl 0.3 mol L−1 for 60 and 80 min have been used successfully for the production of polyhydroxyalkanoates by Cupriavidus necator. The yields of polyhydroxybutyrate were 0.21–0.26 g PHB g−1 reducing sugar consumed and the accumulation of the biopolymer was of the order of 58% dry cell weight.