Pokemon X and Y have introduced a new Game Mechanic in Affection, which can cause Pokemon to do several things in and out of Battle. One of them can be to Evolve certain Pokemon such as Sylveon, and another is to allow the player to view the feelings of a Pokemon during Battle and for that Pokemon to display it's Affection through Shaking before Battle at Level 3 Affection, Jumping at Level 4 Affection, and looking back at the Trainer at Level 5 Affection. This new Mechanic can also cause the Pokemon to land Critical Hits, survive hits at 1 HP, evade hits, and shed off a Status alignment.
As for what effects how a Pokemon feels or what it is interested in during Battle it is currently unknown, but I'm guessing that it depends on two factors- HP and Randomness. At Max HP, my own Pokemon have felt a number of and were interested in a number of things, such as trust in "[Pokemon's Name] trust [Trainer's Name] to come up with the best strategy at full HP, to "{Pokemon's Name] is in a bit of a pinch. It looks like it may cry". The Pokemon will also "wait for your directions" at the beginning of each turn as it's Affection progresses instead of saying "What will {Pokemon] do?".
However, there are solid evidences as to what the Pokemon feels. Below will be what my Pokemon have felt, and what I think may have triggered it to feel that way:
"[Pokemon's Name] is waiting for directions"- 85% sure this replaces the "What will [Pokemon's Name] do?" caption of each battle at 4 Affection**.
"[Pokemon's Name] seems interested in the other Pokemon's scent!"- The other Pokemon is a compatible mate to the other Pokemon, or shares it's IV's with it.
"[Pokemon's Name] is interested in {Trainer's Name]'s Bag!- Might occur when opposing Pokemon hasn't been caught yet.
"[Pokemon's Name] trust [Trainer's Name] to come up with the best Strategy- 90% sure the Pokemon will feel this when it is at a Typing or Level disadvantage.
"[Pokemon's Name] is in a bit of a pinch. It even looks like it may cry."- 100% that a Pokemon feels this when it is in danger of Fainting at Red HP.
"[Pokemon's Name] read [Trainer's Name] mind and avoided the Attack"- I think that this replaces the "[Pokemon's Name] avoided the Attack" caption (except for Fly, Double Team, and similar Moves), and does not necessarily depend on Affection.
"[Pokemon's Name] wants to take some time to play with [Trainer's Name]!"- The Pokemon wants one of it's needs to be met with Amie, either Fullness, Enjoyment, and of course Affection.
And there is one other one that involves the Pokemon cure itself of Status, but I don't quite remember.
As for the others ones, I either have no idea of or have not seen; for now I will leave them to being caused by Randomness (by the ones I do not know).
Furfrou is fine
Is this natural, or is my Furfrou defected?
This is completely natural; every Pokemon with 3 or more Hearts of Affection will experience this.
Source: Experience
DISCLAIMER: This Answer is purely based upon my experiences and speculations alone, so there is a possibility that some or all of it can be incorrect. However, I have given some reasonings of to what I think may be the right answer, so take it with a grain of salt.
