A novel ferromagnetic (CoFe2O4) - ferroelastic (LaCoO3) composite are prepared to enhance the strain sensitivity of the CoFe2O4 for magnetic sensor applications. Backscattered electron micrographs, elemental mapping, XRD and Raman spectra confirm the formation of composites with minimal interdiffusion at the interface between grains of the two constituents. Normalized magnetic hysteresis loops of the composites imply that only ferromagnetic contribution to the loop though the paramagnetic LCO content in the composite alters both the saturation and the coercivity. The shape of λ-curves and the magnitudes of magnetostriction coefficients are changed significantly with an increase in LCO content. Quadratic behavior of the magnetostriction is found to deviate drastically. A model consisting of two interfaces between CFO-LCO-CFO grains is proposed to explain the conversion of bipolar to uni-polar behavior of magnetostriction of CFO. The strain sensitivity of the composites with the low amount of LCO content increased greatly and it is further enhanced on magnetically poled composites at low magnetic fields. This work provides a way to convert magnetostriction response into a uni-polar with a compromise on the magnitude at large fields and to enhance the strain sensitivity at low fields.