The product catalog extensions for products without price (or with price but not for sale directly on website).
With Quote Form your customers will get an option to send an inquiry just for one product at a time.
With Quote Cart you can add multiple products to cart and send an inquiry with all the products listed.
The Product Locations extension is useful if every product should be connected to different email address or location. This way the customer can send an inquiry to the email address assigned for the particular product.