The Payage plugin uses Joomla's text translation system. A language file translates the language constants used by the code, for example "PLG_PAYAGE_RETURN_SUCCESS", to the text value shown to the user, for example (in English), "Thank you for your payment". Joomla automatically loads the correct language file for the site language, if it exists.
The plugin currently only comes with an English language file:
/administrator/language/en-GB/en-GB.plg_content_payage.iniSee the Language Files section for more information about modifying and overriding language files.