We report improved low-field magnetoresistance (LFMR) effects of the $La_{0.7}Sr_{0.3}Mn_{1+d}O_3-Mn_3O_4$ composite films with the nominal composition of $La_{0.7}Sr_{0.3}MnO_3$(LSMO)-50 mol% $Mn_3O_4$. The composite films were fabricated by ex-situ solid phase crystallization (SPC) of amorphous films at the annealing temperature region of $900-1100^{circ}C$ for 2 h in a pure oxygen atmosphere. The amorphous films were deposited on polycrystalline $BaZrO_3$ (poly-BZO) substrates by dc-magnetron sputtering at room temperature. The Curie temperatures ($T_C$) of all composite films were insignificantly altered in the range of 368-372 K. The highest LFMR value of 1.29 % in 0.5 kOe with the maximum dMR/dH value of $37.4%kOe^{-1}$ at 300 K was obtained from 900 nm-thick composite film annealed at $1100^{circ}C$. The improved LFMR properties of the composite films are attributed to effective spin-dependent scattering at the $La_{0.7}Sr_{0.3}Mn_{1+d}O_3$ grain boundaries sharpened by adjacent chemically compatible $Mn_3O_4$ grains.