What could be a snappy equivalent for the French catchphrase "si c'est gratuit vous êtes le produit"?

How about,

if you don't pay you're giving yourself away.

There are many variations, all of which roughly translate to the same as the French you quote. There's no "definitive" version.

A quick Google produces examples including:

If you are not paying for it, you're not the customer; you're the product being sold

https://www.quora.com/Who-originally-suggested-that-if-youre-not-paying-for-the-product-you-are-the-product

If You're Not Paying For It, You Become The Product

http://www.forbes.com/sites/marketshare/2012/03/05/if-youre-not-paying-for-it-you-become-the-product/#7591707eb445

If You're Not Paying for It; You're the Product

http://lifehacker.com/5697167/if-youre-not-paying-for-it-youre-the-product

... so you'd be fine to use "if it's free then you're the product" if that's what you want.

If you're not paying for a product, you are the product.

Try there's no such thing as a free lunch.

It is used for saying that people cannot get something good, especially for free, without working hard or giving something in exchange.

A frequently used adage in the UK is:

If the deal you are being offered seems too good to be true, it probably is.