The performance of composite materials is influenced largely by adding organic or inorganic nanoparticles. The composite properties also depend on the fiber/matrix interface bonding. The present article focuses on the influence of basalt fiber surface modifications using hybrid sizings (silane/and silica nanoparticles (SNPs)) and matrix modifications by adding SNPs in the epoxy resin are studied. Vacuum-assisted resin infusion molding (VARIM) was used to fabricate the basalt fiber/epoxy composites. First, the commercial fibers were washed in acetone to remove the commercial sizing; thereafter, a hybrid sizing (3-Glycidyloxypropyl) trimethoxysilane (GPMS)/SNP was applied using the dip-coating method. The SNPs were dispersed using homogenization and probe sonication before infusion. There is an improvement of about 9.05% and 11.33% in the tensile strength and 2.40% and 4.13% in the tensile modulus of as-received basalt fibers with modified epoxy (ABF/EPSNP) and sized basalt fibers with as-received epoxy resin (SBF/EP) composites, respectively. The flexural strength and modulus have improved by about 30% and 8.5%, respectively. Failure mechanisms were analyzed using scanning electron microscopy. From the current study, it was found that surface modifications could result in better composite performance.