Classic form widget doesn't respect first day of week setting from Drupal

When you refer to "calendar view", do you mean the date input? Or a calendar views display provided by another module?

Yes, I'm referring to the date input, see attached screenshot.

Your browser provides this calendar window, and is related to the language selected.
The same behaviour applies to any date fields.

This module doesn't define the calendar widget for choosing dates. The widget is inherited from Drupal core, and to the point made by @tyapchyc, this is really provided by the browser. As such, it isn't clear what this module could do to address the issue.