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The complex physical, kinematic, and chemical properties of galaxy centres make them interesting environments to examine with molecular line emission. We present new $2-4$" (${\sim}75{-}150$ pc at $7.7$ Mpc) observations at 2 and 3 mm covering the central $50$" (${\sim}1.9$ kpc) of the nearby double-barred spiral galaxy NGC 6946 obtained with the IRAM Plateau de Bure Interferometer. We detect spectral lines from ten molecules: CO, HCN, HCO$^+$, HNC, CS, HC$_3$N, N$_2$H$^+$, C$_2$H, CH$_3$OH, and H$_2$CO. We complemented these with published 1mm CO observations and 33 GHz continuum observations to explore the star formation rate surface density ${Σ_{\mathrm{SFR}}}$ on 150 pc scales. In this paper, we analyse regions associated with the inner bar of NGC 6946 $-$ the nuclear region (NUC), the northern (NBE), and southern inner bar end (SBE) and we focus on short-spacing corrected bulk (CO) and dense gas tracers (HCN, HCO$^+$, and HNC). We find that HCO$^+$ correlates best with ${Σ_{\mathrm{SFR}}}$, but the dense gas fraction ($f_{\mathrm{dense}}$) and star formation efficiency of the dense gas (${\mathrm{SFE_{dense}}}$) fits show different behaviours than expected from large-scale disc observations.The SBE has a higher ${Σ_{\mathrm{SFR}}}$, $f_{\mathrm{dense}}$, and shocked gas fraction than the NBE. We examine line ratio diagnostics and find a higher CO(2-1)/CO(1-0) ratio towards NBE than for the NUC. Moreover, comparison with existing extragalactic datasets suggests that using the HCN/HNC ratio to probe kinetic temperatures is not suitable on kiloparsec and sub-kiloparsec scales in extragalactic regions. Lastly, our study shows that the HCO$^+$/HCN ratio might not be a unique indicator to diagnose AGN activity in galaxies.