Inveo

This plugin will fully integrate your WordPress with no compromises into any web application supported by the Theme Provider module.
Demo (PS 1.7): <a href="http://demo.inveostore.com/prestashop17/blog/" rel="nofollow ugc">demo.inveostore.com/prestashop17/blog/</a>
Demo (PS 1.6): <a href="http://demo.inveostore.com/prestashop16/blog/" rel="nofollow ugc">demo.inveostore.com/prestashop16/blog/</a>
Live websites: http://www.inveostore.com/info/featured-websites-6
Currently supported web apps: PrestaShop 1.3/1.4/1.5/1.6/1.7 (excellent eCommerce store)
You need to install Theme Provider <a href="http://www.inveostore.com/wp-theme-providers" title="PrestaShop Theme Provider module" rel="nofollow ugc">PrestaShop Module</a> on your ecommerce website to use this plugin.
Features:
<ul>
<li>Integrates WordPress to PrestaShop with a simple click</li>
<li>Automatically adjusts WordPress CSS selectors (restricts WordPress styles only to the WordPress elements)</li>
<li>100% compatibility with other WordPress plugins</li>
<li>Editing of the WordPress or PrestaShop template files not required</li>
<li>Produces a valid (X)HTML source code</li>
</ul>
Support thread (PrestaShop): <a href="https://www.prestashop.com/forums/topic/432988-module-wordpress-blog-integration-to-prestashop-13141516/?view=getlastpost" rel="nofollow ugc">www.prestashop.com/forums/topic/432988-module-wordpress-blog-integration-to-prestashop-13141516/?view=getlastpost</a>
You may also like our <a href="http://www.wp-accelerator.com/wordpress-woocommerce-accelerator-47?utm_source=webmedia&utm_medium=directory&utm_campaign=Wordpress.org" title="WordPress & WooCommerce Accelerator" rel="nofollow ugc">WordPress & WooCommerce Accelerator</a> plugin and the <a href="http://www.presta-accelerator.com/prestashop-accelerator-46?utm_source=webmedia&utm_medium=directory&utm_campaign=Wordpress.org" title="PrestaShop Accelerator" rel="nofollow ugc">PrestaShop Accelerator</a> module.
<h3>License</h3>
This plugin is free for everyone! It is released under the LGPL, which means you can use it free of charge on your personal or commercial blog. But in order to enjoy the full functionality of this plugin, you need to download the Theme Provider module for the web app you want to integrate your WordPress with.

WP Integration

This plugin will fully integrate your WordPress with no compromises into any web application supported by the Theme Provider module.

defrone

Displays CATEGORIES of your <a href="http://www.prestashop.com" title="an opensource ecommerce solution" rel="nofollow ugc">PrestaShop</a> ecommerce website on your blog. 
Displays “home categories” (level depth = 1) on your blog.
You need to install the PrestaShop module for WordPress categories on your ecommerce website to use this plugin : <a href="http://prestashop.joelgaujard.info/product.php?id_product=17" title="PrestaShop module for WordPress" rel="nofollow ugc">http://prestashop.joelgaujard.info/product.php?id_product=17</a>
Some functionalities :
<ul>
<li>configure the URL of your PrestaShop ecommerce website</li>
<li>creation of one widget to displays categories</li>
<li>specify if you want to display image category</li>
</ul>
<h3>Arbitrary section</h3>
You must read this tutorial : http://blog.joelgaujard.info/tutorial/tutorial-prestashop-wordpress

WP PrestaShop Categories

Displays CATEGORIES of your [PrestaShop](http://www.prestashop.com "an opensource ecommerce solution") ecommerce website on your blog.

WP Integration vs WP PrestaShop Categories