I looked at both pages, and they both use form #4261
In our plugin, used with WPML, the form must be translated using WPML, so, editing that form in WP Admin, this + button:
https://www.screencast.com/t/PPMXYo6NtNN
once translated, you may need to edit the form and make sure all the settings are correct (fields, and settings within fields) for the new language.
The Results URL will be different also, see the note about the Shortcode method at the foot of this documentation page:
https://searchandfilter.com/documentation/3rd-party/wpml/
Note, if you are using the Shortcode method and a customised results.php template, the template may need to change (to translate some strings for example), and as each form has its own ID, use the numbering method described almost at the end of this documentation page:
https://searchandfilter.com/documentation/search-results/using-a-shortcode/