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.

jotraverso

Provide a sidebar widget for getting content from Prestashop via the REST API and show it with jcarrousell lite.
<h3>Configuration</h3>
The widget need a few integration and behavioural parameters:
<ol>
<li>Prestashop’s web service authorization key. It should be generated from Prestashop’s admin site.</li>
<li>REST query for products. The widget expects a full view result, so the query must include “display=full” parameter.</li>
<li>Prestashop base URL. The Prestashop location URL (without the last bar ‘/’), it’s used when the widget build prestashop’s links.</li>
<li>JCarrousell Lite easing effect. Labeled with “Efecto de transición (easing)”, choose from a value from the dropdown menu.</li>
<li>JCarrousell Auto. Labeled with “Pausa (milisegundos)”, milliseconds to keep every product.</li>
<li>JCarrousell Speed. Labeled with “Velocidad (milisegundos), Number of milliseconds, speed for the transition.</li>
</ol>

Prestashop Saiyandev Widget

Provide a sidebar widget for getting content from Prestashop via the REST API, and show it with jcarrousell.

WP Integration vs Prestashop Saiyandev Widget