You are not able to list a free product through JVZoo. There must be a charge to run a transaction, however you can have a free product be part of your own sales funnel by having an opt-in form. By using the Pre-launch option, you can give away a freebie upon signing up and this will lead to the sales page of a product you have for sale in your funnel. It just cannot be listed as its own product.
Set up a product that you have for sale using the Pre-launch option for the URL of your freebie.
Please be sure to leave the option to automatically send traffic to sales page after launch date off if you want to offer a free product.