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Here's the function I use in my Image/Video Gallery module (modules/nc_gallery/nc_gallery.php):

public function hookDisplayAdminProductsExtra($params)
{
    if (isset($params['id_product']) && (int)$params['id_product']) {
        $controller = new AdminNCGalleryGalleriesController();
        $this->context->smarty->assign('form', $controller->renderProductForm((int)$params['id_product']));

        return $this->display(__FILE__, 'views/templates/admin/tab.tpl');
    }
}

And a simplified version of the renderProductForm function that displays a multi-language text field on the configuration page (modules/nc_gallery/controllers/admin/AdminNCGalleryGalleriesController.php):

public function renderProductForm($id_product)  
{
    if ((int)$id_product <= 0) {
        return;
    }

    $fields_value = [];
    $product_tab = null;
    $id_product_tab = (int)NCGalleryProductTab::getTabForProduct((int)$id_product);

    if ($id_product_tab) {
        $product_tab = new NCGalleryProductTab((int)$id_product_tab);
        $fields_value['nc_gallery_name'] = [];

        foreach (Language::getLanguages(false) as $language) {
            if (is_array($product_tab->name) && isset($product_tab->name[(int)$language['id_lang']]) &&
                $product_tab->name[(int)$language['id_lang']] != '') {
                $fields_value['nc_gallery_name'][(int)$language['id_lang']] =
                    $product_tab->name[$language['id_lang']];
            } else {
                $fields_value['nc_gallery_name'][(int)$language['id_lang']] =
                    Configuration::get('NC_GALLERY_DEFAULT_TAB_TITLE', (int)$language['id_lang']);
            }
        }
    } else {
        foreach (Language::getLanguages(false) as $language) {
            $fields_value['nc_gallery_name'][(int)$language['id_lang']] =
                Configuration::get('NC_GALLERY_DEFAULT_TAB_TITLE', (int)$language['id_lang']);
        }
    }

    $this->fields_form = [
        'input' => [
            [
                'type' => 'text',
                'label' => $this->l('Title'),
                'name' => 'nc_gallery_name',
                'hint' => $this->l('The tab text displayed on the product page'),
                'required' => true,
                'lang' => true,
                'class' => 'form-control',
            ],
        ],
    ];

    $this->fields_form = [['form' => $this->fields_form]];

    $helper = new HelperForm($this);
    $this->setHelperDisplay($helper);
    $helper->languages = Language::getLanguages();
    $helper->default_form_language = (int)Configuration::get('PS_LANG_DEFAULT');
    $helper->fields_value = $fields_value;
    $helper->submit_action = $this->submit_action;
    $helper->tpl_vars = $this->getTemplateFormVars();

    return $helper->generateForm($this->fields_form);
}

And in modules/nc_gallery/views/templates/admin/tab.tpl:

<input type="hidden" name="submitted_tabs[]" value="nc_gallery" />

{$form}

I hope this helps.

Here's the function I use in my Image/Video Gallery module:

public function hookDisplayAdminProductsExtra($params)
{
    if (isset($params['id_product']) && (int)$params['id_product']) {
        $controller = new AdminNCGalleryGalleriesController();
        $this->context->smarty->assign('form', $controller->renderProductForm((int)$params['id_product']));

        return $this->display(__FILE__, 'views/templates/admin/tab.tpl');
    }
}

And a simplified version of the renderProductForm function that displays a multi-language text field on the configuration page:

public function renderProductForm($id_product)  
{
    if ((int)$id_product <= 0) {
        return;
    }

    $fields_value = [];
    $product_tab = null;
    $id_product_tab = (int)NCGalleryProductTab::getTabForProduct((int)$id_product);

    if ($id_product_tab) {
        $product_tab = new NCGalleryProductTab((int)$id_product_tab);
        $fields_value['nc_gallery_name'] = [];

        foreach (Language::getLanguages(false) as $language) {
            if (is_array($product_tab->name) && isset($product_tab->name[(int)$language['id_lang']]) &&
                $product_tab->name[(int)$language['id_lang']] != '') {
                $fields_value['nc_gallery_name'][(int)$language['id_lang']] =
                    $product_tab->name[$language['id_lang']];
            } else {
                $fields_value['nc_gallery_name'][(int)$language['id_lang']] =
                    Configuration::get('NC_GALLERY_DEFAULT_TAB_TITLE', (int)$language['id_lang']);
            }
        }
    } else {
        foreach (Language::getLanguages(false) as $language) {
            $fields_value['nc_gallery_name'][(int)$language['id_lang']] =
                Configuration::get('NC_GALLERY_DEFAULT_TAB_TITLE', (int)$language['id_lang']);
        }
    }

    $this->fields_form = [
        'input' => [
            [
                'type' => 'text',
                'label' => $this->l('Title'),
                'name' => 'nc_gallery_name',
                'hint' => $this->l('The tab text displayed on the product page'),
                'required' => true,
                'lang' => true,
                'class' => 'form-control',
            ],
        ],
    ];

    $this->fields_form = [['form' => $this->fields_form]];

    $helper = new HelperForm($this);
    $this->setHelperDisplay($helper);
    $helper->languages = Language::getLanguages();
    $helper->default_form_language = (int)Configuration::get('PS_LANG_DEFAULT');
    $helper->fields_value = $fields_value;
    $helper->submit_action = $this->submit_action;
    $helper->tpl_vars = $this->getTemplateFormVars();

    return $helper->generateForm($this->fields_form);
}

And in tab.tpl:

<input type="hidden" name="submitted_tabs[]" value="nc_gallery" />

{$form}

I hope this helps.