Foam concrete is widely used due to its excellent thermal insulation properties, but the large amount of cement used in its production process leads to high carbon emissions. This study investigated the effects of recycled concrete powder (RCP) replacement and carbonation curing technology on the properties of foam concrete. After 28 d of standard curing, compared with unsubstituted specimens, the properties of specimens containing 10% (mass fraction) RCP are similar. When the RCP replacement rate is 30% (mass fraction), the porosity of specimens increases by 10.9%, the compressive strength decreases by 21.3%, and the thermal conductivity decreases by 11.7%. Compared with counterparts with 28 d standard curing, the properties differences are minimal after 3 d of carbonation curing. After 7 d of carbonation curing, the porosity of specimens decreases by 4.6%~13.4%, the compressive strength increases by 9.8%~16.7%, and the thermal conductivity increases by 6.4%~11.3%. All specimens meet the specification requirements for non-load-bearing thermal insulation exterior wall materials, surpassing the properties of foam concrete reported in the existing literature. Additionally, this study characterizes the phase assemblage of foam concrete, highlighting the high carbon fixation rate of this novel foam concrete, about 12.99% measured using 5 mm of the surface layer. In summary, combining RCP replacement and carbonation curing significantly improves foam concrete properties and carbon fixation capacity, which helps to prepare a novel low-carbon foam concrete product.