Fate-is-one-edge: It is impossible to purchase a game through the Uplay client.
timppu: Are you sure your information is up to date? At least now when I am logged into the UPlay client, there is a "Store" page there too from where you can add games to your cart etc. I haven't actually bought anything from there but at least to me it seems to work the same as e.g. the Store page on the Steam client. You pick items adding to your cart, go to the Checkout where it asks for billing information blaa blaa blaa. It never launches a web browser at that point.
Fate-is-one-edge: What did you do exactly?
timppu: Pretty much as soon as I logged in, there was an ad for that freebie so I clicked once or twice, after which it was in my account. Try it yourself.
Unfortunately no such advertisement appeared on my Uplay client when I installed it and neither could I find any announcement, concerning that offer on Uplay's newsfeed, or any other sales offer for that matter.
For me, I can only find it on the Ubistore webpage, as part of a special sales period.