Aha, sure, just use the WordPress function for formatting dates in different languages.
$dateformatstring = "l d F, Y";
$unixtimestamp = strtotime(get_field('date_picker'));
echo date_i18n($dateformatstring, $unixtimestamp);
This is dependent on your blog language setting. More info here: http://codex.wordpress.org/Function_Reference/date_i18n
If you can’t set blog language to french, you can also do it with PHP only.
setlocale(LC_ALL, 'fr_FR');
echo strftime("%A %e %B %Y");
Another example with day of week and month (french):
setlocale(LC_ALL, 'fr_FR');
echo strftime("%A le %d %B, %Y");
//with day of the week = mercredi le 18 septembre, 2013
