How to display an asset (pdf) from both site languages on both sites?
You could try and fetch the other pdf by creating an entry query for the different language, and getting the pdf from there.
{# if you have only 2 languages: #}
{% set otherLanguage = craft.entries().id(entry.id).siteId(['not', entry.siteId).one() %}
{{ otherLanguage.PDF.url }}


{# if you have more languages (and want all the PDFs: #}
{% set otherLanguages = craft.entries().id(entry.id).siteId(['not', entry.siteId).all() %}
{% for $otherLanguage in $otherLanguages %}
    {{ otherLanguage.PDF.url }}
{% endfor %}