GaN microwires grown by metalorganic vapour phase epitaxy and with radii typically on the order of 1-5 micrometers exhibit a number of resonances in their photoluminescence spectra. These resonances include whispering gallery modes and transverse Fabry-Perot modes. A detailed spectroscopic study by polarization-resolved microphotoluminescence, in combination with electron microscopy images, has enabled to differentiate both kinds of modes and determined their main spectral properties. Finally, the dispersion of the ordinary and extraordinary refractive indices of strain-free GaN in the visible-UV range has been obtained thanks to the numerical simulation of the observed modes.