Translate placeholder text in search field

Just as any regular string, you can use

<?php esc_attr_e( 'Your Search term here', 'your_theme_slug' ); ?>

So your code for the <input> would look like

<input type="search" class="search-field" placeholder="<?php 
    esc_attr_e( 'Your Search term here', 'your_theme_slug' ); 
    ?>" value="<?php 
    echo esc_attr( $search ); 
    ?>" name="s">

WPML, as well as WordPress, uses the PHP get_text() function. You can translate this either with the additional String Translation Plugin, or you create a mo/po file for your theme.