Green composites made of bioplastics reinforced with natural fibers have gained considerable attention over recent years. However, the use of natural fibers in composites usually compromise some key properties, such as the impact strength and the processability of the final materials. In the present study, two distinct additives, namely an epoxidized linseed oil (ELO) and a sugar-based surfactant, viz. GlucoPure® Sense (GPS), were tested in composite formulations of poly(lactic acid) (PLA) or poly(hydroxybutyrate) (PHB) reinforced with micronized pulp fibers. Both additives showed a plasticizing effect, which led to a decrease in the Young’s and flexural moduli and strengths. At the same time, the elongation and flexural strain at break were considerably improved on some formulations. The melt flow rate was also remarkably improved with the incorporation of the additives. In the PHB-based composites, an increment of 230% was observed upon incorporation of 7.5 wt.% ELO and, in composites based on PLA, an increase of around 155% was achieved with the introduction of 2.5 wt.% GPS. ELO also increased the impact strength to a maximum of 29 kJ m−2, in formulations with PLA. For most composites, a faster degradation rate was observed on the formulations with the additives, reaching, in the case of PHB composites with GPS, a noteworthy weight loss over 75% under burial testing in compost medium at room temperature.