For curing bio-based benzoxazine monomers completely below 200 °C, bio-based phloretic acid (PHA), p-coumaric acid (pCOA), and ferulic acid (FEA) containing a carboxylic group as a phenol source and furfurylamine (FA) as an amine source are used to prepare three full bio-based benzoxazines (PHA-fa, pCOA-fa, and FEA-fa). Differential scanning calorimetry experimental results showed that PHA-fa, pCOA-fa, and FEA-fa possessed low ring-opening polymerization temperatures and △H values and could be cured completely below 200 °C. The obtained full bio-based polybenzoxazines (poly(PHA-fa), poly(pCOA-fa), and poly(FEA-fa)) presented lower decomposition rates and higher residual char at 800 °C. In addition, poly(PHA-fa), poly(pCOA-fa), and poly(FEA-fa) were predicted to have good flame retardancy due to low heat release capacity and total heat release values. From the above results, it is known that natural renewable resources, PHA, pCOA, FEA, and FA, contribute to obtaining high-performance bio-based thermosets with excellent low-temperature curing performance and high char at 800 °C, which make them suitable for applications of plant fiber-reinforced composites.