Simple php search engine for my site

I have a French based language site: http://www.ipeut.com with articles on different categories.

I want to implement a simple php search engine for my website on pages like this on the top right corner:
http://www.ipeut.com/economie/politique-economique/178/marges-de-jeu-et-grandes-optio73122.php
Note: I keep all texts (title, body articles) on a mysql database.

Is there a possibility to integrate Google Site Search?
How can i do that?

I need some code suggestions, to make this script run fast.

Thanks all,