This thread is resolved. Here is a description of the problem and solution.
Problem: How do I translate my cookie plugin strings?
Solution: Please go to WPML > Theme and plugin localization and make sure that either "Translate the theme and plugins using WPML's String Translation only (don't load .mo files)" or "Translate the theme and plugins using WPML's String Translation and load .mo files as backup is selected.
Also, Please go to WPML -> Languages and scroll down to the Language Filtering for Ajax section. Check the box to enable "Store a language cookie to support language filtering for AJAX".
This is the technical support forum for WPML - the multilingual WordPress plugin.