GaN planar nanowires (NWs) are fabricated by selective area metal-organic vapor phase epitaxy using focused ion beam etching of trench pattern in the Si3N4 mask. Two crystallographic orientations of NWs along [1120] and [1010] directions are investigated. The coherent growth is confirmed for both directions; however, the best morphology, crystalline and optical properties are found in the GaN planar NWs fabricated along the [1010] axis. Cathodoluminescence (CL) at 5K reveals a presence of Fabry-Perot modes in the region of 1.8-2.5 eV for the NWs fabricated in the [1010] direction. The position and intensity of the Fabry-Perot peaks vary depending on measured point within the NW, which is explained by the model based on the Purcell coefficient calculations. It is shown that small fluctuations in the NW thickness cause a noticeable shift of the Fabry-Perot modes energies, while the enhancement or reduction of the emission intensity for the Fabry-Perot peaks depend on the position of the emitter inside the planar NW.