Reading the example on Zurb’s docs, I get the impression that you would take this code and break it up into smaller templates like how the _s theme does it.
Starting in your header.php
<div class="off-canvas-wrap">
<div class="inner-wrap">
Then using get_template_part() for example a template named tab-bar could be:
<nav class="tab-bar">
<section class="left-small">
<a class="left-off-canvas-toggle menu-icon" ><span></span></a>
</section>
<section class="middle tab-bar-section">
<h1 class="title">Foundation</h1>
</section>
<section class="right-small">
<a class="right-off-canvas-toggle menu-icon" ><span></span></a>
</section>
</nav>
Then another template named left-off-canvas could call:
<aside class="left-off-canvas-menu">
<ul class="off-canvas-list">
<li><label>Foundation</label></li>
<li><a href="#">The Psychohistorians</a></li>
</ul>
</aside>
And yet another template could call the right off canvas.
<aside class="right-off-canvas-menu">
<ul class="off-canvas-list">
<li><label>Users</label></li>
<li><a href="#">Hari Seldon</a></li>
</ul>
</aside>
Next in your index.php file you can then call the loop with your main content
<section class="main-section">
<!-- MAIN CONTENT GOES HERE -->
</section>
Then close it all off in your footer.php
<a class="exit-off-canvas"></a>
</div>
</div>
Using templates this way can really break up and keep the modularity your looking for.