Changing the argument of a function

Try: (add to functions.php of your theme)

add_filter( 'woocommerce_breadcrumb_defaults', 'wpse_woocommerce_breadcrumb_defaults' );
function wpse_woocommerce_breadcrumb_defaults( $args ) {
    $args['wrap_before'] = '<nav class="woocommerce-breadcrumb my-class">';
    $args['wrap_after'] = '</nav>';

    return $args;
}

Or, copy:

wp-content/plugins/woocommerce/templates/global/breadcrumb.php

to

wp-content/themes/your-theme/templates/global/breadcrumb.php

UPDATE: This is the correct path and not above: (thanks @mmm)

wp-content/themes/your-theme/woocommerce/global/breadcrumb.php

and change the echo $wrap_before; and echo $wrap_after; to your liking..

Reference: https://docs.woocommerce.com/document/template-structure/