This code example doesn't handle saving the value. To properly store this setting, register it in the default options array using the frm_default_field_options filter or create your own saving handler

add_action( 'frm_text_primary_field_options', 'custom_field_settings' );
function custom_field_settings( $args ) {
	$field = $args['field'];
	$custom_setting = isset( $field['custom_setting'] ) ? $field['custom_setting'] : '';
	?>
	<p>
		<label for="custom-setting-<?php echo intval( $field['id'] ); ?>">
			<?php esc_html_e( 'Custom setting', 'text-domain' ); ?>
		</label>
		<input type="text" id="custom-setting-<?php echo intval( $field['id'] ); ?>" name="field_options[custom_setting_<?php echo intval( $field['id'] ); ?>]" value="<?php echo esc_attr( $custom_setting ); ?>" />
	</p>
	<?php
}

add_filter( 'frm_default_field_options', 'add_custom_field_option', 10, 2 );
function add_custom_field_option( $options, $args ) {
	if ( 'text' === $args['type'] ) {
		$options['custom_setting'] = '';
	}
	return $options;
}