Product Registration Card?

In my cd case I also have this red black slip of paper that says,

...

SQUARE ENIX MEMBERS
http://member.square-enix.com/n/ Product Registration Card
(something in French) then:

Thank you for purchasing a SQUARE ENIX product. The below code is your SQUARE ENIX Members redemption code, which allows you to become a part of our exclusive Members community. Join today to receive exclusive news, promotional offers and entry into exclusive contests and sweepstakes.

(something in French)

Then a serial code.

...

What is this? Do I need it? Like if a gold seller were to steal my account would this be useful to prove I actually bought the product? I don't do sweepstakes because I'm not into chance and luck. Should I just ignore this? What good would a product registration do me anyway?

That's just an optional thing - it just adds the game to your profile on the SE Member's site on the SE main website for your region (if you have a French version, I presume you're in Europe so hence it would be the Square Enix Europe website. But you don't have to do that if you do not wish to, it's just something extra some players like to do.

It's just to display what games you have on the SE social page - have no impact on the usability of the game or anything else account related so you can indeed skip that entirelly.