Saving a field of type 'text_format' as a theme settings variable
Text format fields are considered to be a compound field (meaning that multiple values are stored for the one field -- the value and the format).

If you inspect the value of mytheme_texte_presentation, you'll find an array that looks something like this array =&gt; ['value' =&gt; '&lt;val&gt;', 'format' =&gt; 'html_restreint']. 

If you look at the docs for text_format, you'll see that there is a #format attribute.

Your code should look something like this: 

$texte_presentation = theme_get_setting('mytheme_texte_presentation');
$form['mytheme_texte_presentation'] = array(
    '#type'          =&gt; 'text_format',
    '#title'         =&gt; t('Test theme settings'),
    '#default_value' =&gt; $texte_presentation['value'],
    '#format'        =&gt; $texte_presentation['format'],
    '#description'   =&gt; t("lorem ipsum"),
  );


Note: This is untested code. You may need to tweak this a bit to make it functional.