There is a php library[1], you’ll probably need to use the advanced library[2].
You can see here that in fact there are ways to translate the PDF file[3]. Google uses these examples because works faster and more efficiently with this language libraries.
You could link the PDF’s to:
http://translate.google.com/translate?hl=fr&sl=auto&tl=en&u=http://www.example.com/PDF.pdf
Using the following parameters:
hl -> Original Language.
tl -> Translate Language.
u -> PDF URL
[1]https://cloud.google.com/translate/docs/reference/libraries/v3/php
[2]https://github.com/googleapis/google-cloud-php-translate
[3]https://cloud.google.com/translate/docs/advanced/translate-documents