Steps to reproduce:

1. Add an ezdate fieldtype to any Content Type.
2. Change a Back Office language to French.
3. Create a content of the Content Type mentioned in step 1, and pick any date (for example 14.10.2022) in the ezdate field.

Result:
A Flatpickr instance is localized properly, an input value in a field is not localized after a selection.

Expected result:
One should see octobre 14, 2022 instead of October 14, 2022 in an input.

Note:
Properly localized date is displayed in a content's preview so this is just a matter of form input.