How to place copyright next to footer menu?

You can achieve this by enclosing them in divs like in following line of your code

<p id="copyright">&copy; <?php echo date('Y');?> <?php bloginfo('name'); ?> | <?wp_nav_menu( array( 'theme_location' => 'new-menu', 'container_class' => 'secondary-footer' ) ); ?></p>

Enclose above code in divs like this

<div style="float:left;width:50%;"><p id="copyright">&copy; <?php echo date('Y');?> <?php bloginfo('name'); ?> | </div>
<div style="float:left;width:50%;"><?wp_nav_menu( array( 'theme_location' => 'new-menu', 'container_class' => 'secondary-footer' ) ); ?></p></div>

Note: You have to adjust your Paragraph tag (with id="copyright") between these divs.

UPDATE

You can make text closer with the help of padding property of css like this
If you wanna move text of div to the right side then use padding-left:5%;. For example:

<div style="float:left;width:50%;padding-left:5%;">

And If you wanna move text of div to the left side then use padding-right:5%;. For example:

<div style="float:left;width:50%;padding-right:5%;">

Padding property is use to move contents/text of div (not div itself) to any direction (left, right, top, bottom).

Note: You need to specify Padding’s value (for demo I gave 5%) as per your need. So change the value. And also don’t forget to make classes of these divs, Because it would be better if you use these css properties in classes instead of Style inside div.

As an alternate you can reduce the width of div also to make them closer.