Translation of months and days in Calendar Views Module The Views Calendar template displays months and days, i.e. June, July, Monday, Tuesday,  etc.

When someone changes from english to french, how can I tell it to display the months in a different language?
You need to translate the strings. Go to Administration » Configuration » Regional and language » Translate interface, in the menu.

Then search for !month-name and !day-abbreviation and translate the strings to your language.

You can also download translations for the whole module on https://localize.drupal.org/translate/languages/fr

You can also use the Localization update module. From the UI of the module you can download and keep track of new translations for your downloaded modules.