solution for prestashop 1.7.81 to 1.7.8.3 (at this time) :
edit classic/templates/checkout/checkout.tpl
and remove
{block name='header'}
{include file='checkout/_partials/header.tpl'}
{/block}
before :
Quote{extends file=$layout}
{block name='header'}
{include file='checkout/_partials/header.tpl'}
{/block}
{block name='content'}
<section id="content">
<div class="row">
<div class="cart-grid-body col-xs-12 col-lg-8">
{block name='checkout_process'}
{render file='checkout/checkout-process.tpl' ui=$checkout_process}
{/block}
</div>
<div class="cart-grid-right col-xs-12 col-lg-4">
{block name='cart_summary'}
{include file='checkout/_partials/cart-summary.tpl' cart=$cart}
{/block}
{hook h='displayReassurance'}
</div>
</div>
</section>
{/block}
{block name='footer'}
{include file='checkout/_partials/footer.tpl'}
{/block}
after :
Quote{extends file=$layout}
{block name='content'}
<section id="content">
<div class="row">
<div class="cart-grid-body col-xs-12 col-lg-8">
{block name='checkout_process'}
{render file='checkout/checkout-process.tpl' ui=$checkout_process}
{/block}
</div>
<div class="cart-grid-right col-xs-12 col-lg-4">
{block name='cart_summary'}
{include file='checkout/_partials/cart-summary.tpl' cart=$cart}
{/block}
{hook h='displayReassurance'}
</div>
</div>
</section>
{/block}
and Tadaaa !