The Cornerstone is not compatible with Polylang at the moment. There are some efforts on our part to make sure the Polylang does not hijack the WPML triggers which fixed some customer issues:
But unfortunately, the system is not compatible with that plugin yet. It may take much time to be able to make the system compatible with the plugin as it may need a great amount of the code refactoring.
That is why I suggest that you use the WPML plugin as an alternative.