enqueue_scripts() in child theme doesn’t work

Technically, your problem (as already pointed out) is that you are using a function that echos instead of returns your path. However, the use of bloginfo/get_bloginfo to retrieve theme directory paths is long since discouraged.

• ‘stylesheet_url’ – Displays the primary CSS (usually
  style.css) file URL of the active theme. Consider echoing get_stylesheet_uri() instead.
• ‘stylesheet_directory’ – Displays the stylesheet
  directory URL of the active theme. (Was a local path in earlier
  WordPress versions.) Consider echoing
  get_stylesheet_directory_uri() instead.
• ‘template_url’ / ‘template_directory’ – URL of the
  active theme’s directory (‘template_directory’ was a local path before
  2.6; see get_theme_root() and get_template() for hackish alternatives.) Within child
  themes, both get_bloginfo(‘template_url’) and get_template() will
  return the parent theme directory. Consider echoing
  get_template_directory_uri() instead (for the parent template
  directory) or
  get_stylesheet_directory_uri() (for the child template directory).

http://codex.wordpress.org/Function_Reference/bloginfo

As per the Codex section just quoted, the equivalent, correct code should use get_template_directory_uri():

function enqueue_scripts() {
  if ( ! is_admin() ) {
    $scriptsrc = get_template_directory_uri() . '/scripts.js'; 
    wp_register_script( 'scripts', $scriptsrc );
    wp_enqueue_script( 'scripts' );
  }
}
add_action( 'wp_enqueue_scripts', 'enqueue_scripts' );

Note that get_template_directory_uri() will always return a path to the parent theme. If you wish for a child theme to be able to override this file, need get_stylesheet_directory_uri()

Additionally, please do not use a function name as generic as enqueue_scripts. That is likely to cause trouble and is bad practice.