The problem with integrating Zen Cart with an existing site is that if someone is shopping and leaves Zen Cart to visit another part of your site, his/her session and cart contents can be lost. I'm not saying it can't be done. I'm sure someone will chime in to give you pointers on how to accomplish it. I'm just pointing out a possible pit fall.

You can always install Zen Cart in its own folder and then provide a link on the existing site to the Zen Cart portion.