If you have a stress-strain curve for your samples, calculating the young modulus is simple. Identify the linear region of the curve that corresponds with Hooke's law. Then, determine the slope of the linear part of the curve, which represents the young modulus. ( E = stress/strain )
Unlike metallic materials, composite materials like GFRP & CFRP have low strain to failure. Even the initial stress/strain graph is not likely to be linear. The Young's modulus will be different for different range of strains.
ASTM D3039 is the standard for tensile strength & tensile modulus of composite materials. It stipulates 0.1% to 0.3% strain range for the computation of E.
The composite products are designed generally to work in the strain range of 0.1% to 0.3%. Hence the young's modulus is the difference in stress in the 0.1% to 0.3% strain range divided by 0.002 strain.
What are the fibre and the matrix in your composite specimen?