Does your header.php in your child theme contain only this line?
You must copy paste all the content of the original header.php in the file of your child theme and just add:
<ul><?php pll_the_languages(); ?></ul>
where you want it, for example after:
</hgroup>
(that would be pure luck that you want it here).
Then you will need to add CSS rules to design it as you want.