WordPress Customizer select control with published Formidable forms.

formidable-forms-select.php

$forms = FrmForm::get_published_forms();
$choices = array();

foreach ( $forms as $form ) {

  $choices[$form->id] = $form->name;

}

// Formidable Forms Select Field
$wp_customize->add_setting(
	'formidable_form_select',
	array(
		'capability' 		=> 'edit_theme_options',
		'default'  			=> '',
		'transport' 		=> 'postMessage',
		'type' 				=> 'theme_mod'
	)
);

$wp_customize->add_control(
	'formidable_form_select',
	array(
		'active_callback' 	=> '',
		'choices' 			=> $choices,
		'description' 		=> esc_html__( '', 'text-domain' ),
		'label'  			=> esc_html__( 'Formidable Forms Select', 'text-domain' ),
		'priority' 			=> 10,
		'section'  			=> 'your-section',
		'settings' 			=> 'formidable_form_select',
		'type' 				=> 'select'
	)
);

$wp_customize->get_setting( 'formidable_form_select' )->transport = 'postMessage';