As bland as it may sound: the Langmuir isotherm is valid when it fits. If you see that there is serious deviation, there must be other interactions being in place: Langmuir is for the case that the adsorbate is only bound to the adsorbent, has negligible lateral interaction and no multilayer adsorption. For multilayers, BET would be the option of choice. Lateral interactions are included in Fowler-Frumkin, but that may create unphysical loops.

Freundlich fitting does not say much, since you can have any exponent, you can create a seeming fit for quite many scenarios.

I would also say that the lack of adequate fitting is a sufficient reason to omit the Langmuir model: neither maximal capacity nor sorption affinity make sense, and further only contradictions will be expected, such as temperature dependence of the maximal capacity and inability to account for competitive effects. Indeed, there are plenty of other models to be used. Nevertheless, if the Freundlich model stands against the statistical check, i.e., it fits the experimental data, the RMSD is at the level of the data scatter, and there are no obvious trends in the distribution of residuals (i.e., deviations of experimental values from the theoretical ones), I would definitely consider it useful. If the physical system allows considering a multiplicity of sorption sites acting independently, and each site may be assumed to follow the Langmuir model, then, the Freundlich mode with an exponent less than 1l has a precise interpretation, i.e., an exponential distribution of sorption sites by energy. In order to perform the thermodynamic analysis, it may also be used by using a (concentration-dependent distribution coefficient) which will define the free energy of a transfer from a reference state to a sorbed state. If the exponent is greater than one, than, we deal with cooperative interactions where BET will be a part of the story....