  Bouchet conjectured in 1983 that every flow-admissible signed graph admits a
nowhere-zero 6-flow which is equivalent to the restriction to cubic signed
graphs. In this paper, we proved that every flow-admissible $3$-edge-colorable
cubic signed graph admits a nowhere-zero $10$-flow. This together with the
4-color theorem implies that every flow-admissible bridgeless planar signed
graph admits a nowhere-zero $10$-flow. As a byproduct, we also show that every
flow-admissible hamiltonian signed graph admits a nowhere-zero $8$-flow.
