Jeremy Herve on "[Plugin: Jetpack by WordPress.com] Contact Form not working"

Could you try to deactivate all other plugins, one at a time, and let me know if you find a conflicting plugin?

If that doesn't help, could you open your browser's Javascript console, and check for errors when you click on the button in the form builder? You can follow the instructions here to learn how to enable the Javascript Console in your browser:
http://webmasters.stackexchange.com/questions/8525/how-to-open-the-javascript-console-in-different-browsers

Thanks!