Have you solved it?
Later edit:
Found the issue!
All values from this form must be declared in a key like this fields_value. Look here for example:
$form = [ 'form' => [ 'legend' => [ 'title' => 'Adaugare oferta', ], 'input' => [ [ 'name' => 'bav_title', 'type' => 'text', 'label' => $this->l('Titlu'), 'size' => 500, 'required' => true, ], [ 'name' => 'bav_image', 'type' => 'file', 'label' => $this->l('Imagine'), 'required' => true, 'value' => '' ], [ 'name' => 'bav_subtitle_row_1', 'type' => 'text', 'label' => $this->l('Subtitlu 1 (bold)'), 'value' => '', 'size' => 500, ], [ 'name' => 'bav_subtitle_row_2', 'type' => 'text', 'label' => $this->l('Subtitlu 2'), 'size' => 500, ], [ 'name' => 'bav_description', 'type' => 'textarea', 'label' => $this->l('Descriere'), 'size' => 5000, ], [ 'name' => 'bav_product_link', 'type' => 'text', 'label' => $this->l('Link produs'), 'size' => 2000, ], [ 'name' => 'bav_sort_order', 'type' => 'text', 'label' => $this->l('Ordine sortare'), 'size' => 10, ], [ 'name' => 'bav_is_visible', 'type' => 'select', 'label' => $this->l('Este vizibil'), 'options' => ['1' => 'Da', '0' => 'Nu'], ], [ 'name' => 'bav_start_on', 'type' => 'date', 'label' => $this->l('Oferta incepe pe'), ], [ 'name' => 'bav_expires_on', 'type' => 'date', 'label' => $this->l('Oferta expira pe'), ], ], 'fields_value' => [ // fixes undefined notices in smarty (is looking here to fill form with values) 'bav_title' => '', 'bav_image' => '', 'bav_subtitle_row_1' => '', 'bav_subtitle_row_2' => '', 'bav_description' => '', 'bav_product_link' => '', 'bav_sort_order' => '0', 'bav_is_visible' => '1', 'bav_start_on' => '', 'bav_expires_on' => '', ], 'submit' => [ 'title' => 'Adauga',//$this->l('Save'), 'class' => 'btn btn-default pull-right', ], ] ];
I know this answer may not help you as two years passed, but it may help others.