Combining observations of multiple CO lines with radiative transfer modelling is a very powerful tool to investigate the physical properties of the molecular gas in galaxies. Using new observations and literature data, we provide the most complete CO ladders ever generated for eight star-forming regions in the spiral arms and inter-arms of the spiral galaxy NGC 6946, with observations of the CO(1-0), CO(2-1), CO(3-2), CO(4-3), CO(6-5), (CO)-C-13(1-0) and (CO)-C-13(2-1) transitions. For each region, we use the large velocity gradient assumption to derive beam-averaged molecular gas physical properties, namely the gas kinetic temperature (T-K), H-2 number volume density (n(H-2)) and CO number column density (N(CO)). Two complementary approaches are used to compare the observations with the model predictions: chi(2) minimization and likelihood. The physical conditions derived vary greatly from one region to the next: T-K = 10-250 K, n(H-2) = 10(2.3)-10(7.0) cm(-3) and N(CO) = 10(15.0)-10(19.3) cm(-2). The spectral line energy distribution (SLED) in some of these extranuclear regions indicate a star formation activity that is more intense than that at the centre of our own Milky Way. The molecular gas in regions with a large SLED turnover transition (J(max) > 4) is hot but tenuous with a high CO column density, while that in regions with a low SLED turnover transition (J(max) <= 4) is cold but dense with a low CO column density. We finally discuss and find some correlations between the physical properties of the molecular gas in each region and the presence of young stellar population indicators (supernova remnants, H II regions, H I holes, etc.).