This study presents an X-ray spectropolarimetric characterisation of the Z source GX 340+0 during the normal branch (NB) and compares it with that obtained for the horizontal branch (HB), using IXPE, NICER, and NuSTAR observations. The analysis reveals significant polarisation, with polarisation degrees of ∼1.4% in the NB and ∼3.7% in the HB, indicating a notable decrease in polarisation when transitioning from the HB to the NB. The polarisation angles show a consistent trend across the states. Spectropolarimetric analysis favours a dependence of the polarisation on the energy. The Comptonised component shows similar polarisation in both the HB and NB and is higher than the theoretical expectation for a boundary or spreading layer. This suggests a contribution from the wind or the presence of an extended accretion disc corona (ADC) to enhance the polarisation. The results obtained here highlight the importance of using polarimetric data to better understand the accretion mechanisms and the geometry of this class of sources, providing insights into the nature of the accretion flow and the interplay between different spectral components. Overall, the findings advance our understanding of the physical processes governing accretion in low-mass X-ray binaries.