I read the HQS guide and fought like mad to get the Chateau. I have it at level 5 at the moment and it is...underwhelming.
For one, the rewards are random.
Two, the chances for getting rewards are not divided equally. FP's and medals are fairly uncommon. That means you are much more likely to get supplies and coins than FP's and medals from HQS.
Three, the Chateau does not influence FP amount gained from quests. You will always receive a 5 FP pack regardless of how high your CF is. There's been only a few days where I've gotten more than 2 FP Packs in a day, but mostly it's either 1, 2, or none.
I've had this building for about a month now and I really haven't seen the perpetual motion thing kick in. It's decent in that the goods that I do get aren't tied to goods boosts and so I can get a fair amount of every good. Aside from that, it seems more useful for coins and supplies than goods. I've heard some mention UBQ's, but they are far to expensive to spam for the same reasons. The rewards are random, the chances of each rewards are different, and I will likely come out of it getting supplies and coins rather than goods and medals.
Unless I'm missing something. I'm a little apathetic about it at the moment. I should have went with the attack build...