In practice, this feature is apparently bugged, as users have begun reporting that after spending all of the Farm Cash necessary to win the Mystery Game's six animals, the French Unicorn is then nowhere to be found. For now, Zynga has labeled the issue as "known" but doesn't offer any work-around other than contacting Zynga Customer Support if you're one of the unlucky players to lose your French Unicorn after investing so much to receive it. It's likely that they'll be able to manually generate a French Unicorn in your Gift Box for you, so don't count that option out.
That all being said, right now we're all just left to sit tight until this issue can be resolved, hopefully with plenty of time left to spare to play the game. We haven't been told if contacting Zynga Customer Support is actually mandatory, so if you don't feel like bugging them (or have had rocky experiences in the past), I suppose you could hold out until the issue has been fixed and see if the game recognizes to give you a French Unicorn anyway. Whether or not you want to take that risk, though, will be up to you.
Did you receive your French Unicorn as promised for earning the six other animals, or are you waiting for Zynga to resolve this issue before you even play? Was Customer Support able to resolve your missing French Unicorn problem? Sound off in the comments.