Because of the way PayPal accepts payments, you are not able to list a free product through JVZoo. Paypal requires there 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.