Language Switcher text

Yes, most sites are not very user friendly with language switchers.

Most English speakers are not going to know that Anglais is 'English' unless they have studied French.

Like I say, I've been that guy who has been searching a site for the English link, and not finding it because it wasn't in English. It's just sloppy, and bad UX.

Are you using core Language switcher block or Language switcher module?

The following works for me on an (almost) clean D7 install:

Install, clear cache, switch languages to and fro so that strings get picked up by translation system, navigate to Configuration > Translate interface > Translate and look for 'English' and 'French' there.

seod.info:

name = Speak English Or Die
description = Makes language switcher links translatable, so that they can be in currently viewed language.
package = Other
core = 7.x

seod.module:

<?php

function seod_language_switch_links_alter(&$links, $type, $path) {
  foreach ($links as &$language) {
    switch ($language['title']) {
      case 'English':
        $language['title'] = t('English');
        break;
      case 'Français':
        $language['title'] = t('French');
        break;
    }
  }
}

note: .module files do not have closing ?> tag.

The trick here is one cannot pass variables to translation system via t(), so we need to pass each string explicitly.

You can change the module name if you want :) but the first part of function name must be equal to module name.