High-resolution time-of-flight powder neutron diffraction and high-field magnetization were measured to investigate the magnetic structure and existence of a field-induced magnetic phase transition in the distorted kagome antiferromagnet Cs2Cu3SnF12. Upon cooling from room temperature, the compound undergoes a structural phase transition at Tt=185K from the rhombohedral space-group R3̄m with the perfect kagome spin network to the monoclinic space-group P21/n with the distorted kagome planes. The distortion results in three inequivalent exchange interactions among the S=1/2Cu2+ spins that magnetically order below TN=20.2K. Magnetization measured with a magnetic field applied within the kagome plane reveals small in-plane ferromagnetism resulting from spin canting. On the other hand, the out-of-plane magnetization does not show a clear hysteresis loop of the ferromagnetic component nor a prominent anomaly up to 170 T with the exception of the subtle kneelike bend around 90 T, which could indicate the 1/3 magnetization plateau. The combined analysis using the irreducible representations of the magnetic space groups and magnetic structure refinement on the neutron powder-diffraction data suggests that the magnetic moments order in the magnetic space-group P21′/n′ with the all-in-all-out spin structure, which by symmetry allows for the in-plane canting, consistent with the in-plane ferromagnetism observed in the magnetization.