Jetpack uses a [contact-form] shortcode to create the form. I've seen an issue like this before.
Unfortunately, I am not a Jetpack user, so I can't tell you how to configure it or even check that it's right. Hopefully Jeremy Herve (@jeherve) see this and can chime in. You might want to repost this in the Jetpack support forum.
If it's not a Jetpack problem I can help you with the email configuration part.