Sorry but I’m still not understanding what you did in your blog.
If you created distinct CUSTOM forms which you recall with [newsletter_form form=”X”] you should see in that page just the code you saved in the forms panel at the text area number X.
Of course, as said, do not use [newsletter][newsletter_form form=”X”][/newsletter], that is an incorrect syntax.
When you use custom forms (a custom form MUST contain all the form HTML code with every fields), only that code should be shown. Newsletter does not add other parts. And you should not use on custom form the {subscription_form} tag since it is just a placeholder for the custom form.
Finally, if you use only the [newsletter_form] shortcode without ANY form number, the standard form is generated. That form is translated using the current frontend language using the translations you provided, for each language, in the form fields configuration panel.
If that is not happening, or the translations has not been added or the language detection is not working. If you provide a page (address) with a form and where there is the polylang language switcher, we can check it.
Stefano.
ps: as said there could be bugs with the use of custom forms and a multilanguage site, since the multilanguage support is rather invasive on a plugin code, but checking online could be of help.