Hello again. Please disregard previous post; all described errors or discrepancies are now working as expected, even though I did not make any changes. I suspect the browsers caches were causing the issue.
While testing some more, I found a related issue, that is when you click on the meta link “Inscription” (or “Register” on the English version of the site) you’re redirected on the enrollment page of the main site, which is configured in English, wp-signup.php. Will keep researching on a way to make this php language aware.