You say you don't have access to the main site code, but you can get it just by doing a view source. The header section has this HTML:
HTML Code:
<header>
<div class="main wrap">
<h1><a href="index.html"><img src="images/logoFDQ.png" alt=""></a></h1>
</div>
<nav>
<ul class="menu">
<li class="current"><a href="index.html">Accueil</a></li>
<li><a href="membres.html">Devenez membre</a></li>
<li><a href="form-partenaires.html">Devenez partenaire</a></li>
<li><a href="contact.html">Nous contacter</a></li>
</ul>
<ul class="reseaux"> <a href="archives.html"><img src="images/pdf.jpg" width="37" height="26"></a> <a href="https://www.facebook.com/fc4x4q?fref=ts" target="_blank"><img src="images/facebook.jpg" width="37" height="26"></a><a href="https://www.youtube.com/user/FC4X4Q" target="_blank"><img src="images/youtube.jpg" width="37" height="26"></a> <a href="chroniques/chroniques_1.html"><img src="images/baroudeur_2.jpg" width="59" height="26"></a>
</ul>
<div class="clear"></div>
</nav>
</header>
You would take everything between (not including) the <header> and </header> tags and put it in tpl_header.php in the area where the logo was. You will need to change hrefs to full web addresses, and either put the images in the ZC /images/ folder or expand those to full URLs.
HTML Code:
<a href="archives.html"><img src="images/pdf.jpg" .../>
<a href="http://www.fc4x4q.com/archives.html"><img src="http://www.fc4x4q.com/images/pdf.jpg" .../>
You will also need to add the relevant style rules from your main site stylesheet to your Zen Cart stylesheet. You can get these, if you don't already have them, by installing Firefox and its Firebug extension, and viewing the CSS. Right-click, Inspect with Firebug will show all the rules that apply to any element you select. Other browsers also have developer tools which you may use if you know how.