The management of red mud (bauxite residue, RM) is critical for environmental protection due to its high alkalinity (pH 12.5–13.0). The study investigates the valorization of RM from the ALUM Tulcea unit (Romania) through accelerated wet carbonation processes (L/S ratio 4:1) and its integration into sustainable construction materials (paving stones). The results indicate a reduction the pH to a stable level of 8.6 in 240 min, a process validated by the formation of new mineral phases (calcite and dawsonite) that stabilize the residual sodium. For the optimized recipe S2 (20% RM, 12% cement, 48% fly ash), an average compressive strength of 33.8 MPa (class T5 according to SR EN 1338:2004) and a low water absorption of 4.12% (Class B) were obtained. Durability tests confirmed superior freeze–thaw resistance (mass loss 0.58 kg/m²) and sodium (Na⁺) leaching below 2.1 mg/L, well below EU limits. In the case of alkaline activated geopolymers (NaOH 8 M), the strength reached 38.5 MPa. The study demonstrates that carbonated RM can reduce the carbon footprint by 20–56% and production costs by up to 43%, providing a viable circular economy solution in line with EU 2030 targets.