For this answer to help you'll need to be able to access the chosen language using javascript. If the language that has been chosen by the user is in the querystring, check out this postthis post.
By adding a Content Editor Web Part to the form and referencing an HTML file that contains the necessary javascript / jquery, the NewForm.aspx labels can be updated. If you're new to working with jQuery in SharePoint, this blog shows how to setup this solution.
You could use this JQuery selector to find the email label and set it to the French version:
$('td.ms-formlabel h3.ms-standardheader nobr:contains("email")').text('Adresse E-mail');
If you haven't used it before, check out Internet Explorer Developer Tools. It will help you when writing other jQuery selectors (try hitting the F12 key when IE is open).