UCoGe exhibits superconductivity in the presence of ferromagnetism. When a field is applied along the b axis (perpendicular to the easy axis), ferromagnetism is weakened and superconductivity is enhanced. This enhancement has been attributed to an increase in coupling as observed in the enhanced effective mass produced by the critical fluctuations as the ferromagnetic transition is strongly suppressed. However it is also important to know if and how the Fermi surface changes near the critical point. Here we report measurements of the thermoelectricity of UCoGe which reveal a low carrier density metal. Under magnetic field applied along the b axis, a sharp peak is observed in the thermopower of UCoGe at H*=11.1T and low temperature which becomes broader at higher temperatures. At higher field, the thermopower changes sign which suggests a modification of the Fermi Surface. We analyze these results using a topological change in Fermi surface and show that this can explain both the thermopower and the enhanced superconductivity.