P&T Contact Form plugin: How to display error messages in other languages via Ajax The validations error message get displayed in main language instead of being translated, you can try here (contact form at bottom):
http://lequartiergeneral.be/en/

The form is being displayed and get response via Ajax.

How to display them correctly in each language?

Thanks
Well, the problem was that I was posting my Ajax request to / from all languages, therefore the site replied back with the site main language, which was French in my case.

The following finally works:

// Get the proper url to post to

if ( '{{ craft.i18n.getCurrentLocale() }}' == '{{ craft.i18n.getPrimarySiteLocale() }}' {
     var url = '/';
} else {
     var url = '/{{ craft.i18n.getCurrentLocale() }}/';
}

// Send it to the server

$.post(url, data, function(response) {
     .......
});