This research investigates the effectiveness of bio-sourced flax fiber-reinforced polymer in comparison with a traditional system based on carbon fiber-reinforced epoxy polymer in order to confine recycled aggregate concretes. The experimental investigation was conducted on two series of concrete including three mixtures with 30%, 50%, and 100% of recycled aggregates and a reference concrete made with natural aggregates. The concrete mixtures were intended for a frost environment where an air-entraining agent was added to the mixture of the second series to achieve 4% air content. The first part of the present work is experimental and aimed to characterize the compressive performance of confined materials. The results indicated that bio-sourced composites are efficient in strengthening recycled aggregates concrete, especially the air-entrained one. It was also found that the compressive strength and the strain enhancement obtained from FRP confinement are little affected by the replacement ratio. The second part was dedicated to the analytical modeling of mechanical properties and stress–strain curves under compression. With the most adequate ultimate strength and strain prediction relationships, the full behavior of FRP-confined concrete can be predicted using the model developed by Ghorbel et al. to account for the presence of recycled aggregates in concrete mixtures.