You become really observant if you make a Puyo Puyo in a Nutshell video.
Accord's hammer here is fusion of her Fever 1 design (and only her Fever 1 design (shown above)) and Popoi below.
See?
So in Puyo Quest Popoi is carrying a design quirk artifact. I think that's neat. Black/Evil Popoi is the most Fever 1 design in the game anyways, let'm have it.
Also, Fever 1 has a bit of a light heaven and hell motif.
So that hammer is combining heaven and hell to bonk Raffina on the head.
(Look, I don't know how true this all is, but you can't deny there's an element of duality in the visual department with Accord and Popoi in this game that got lost in later installments.)
There are many references to the French language in Primp Town (Amitie, Accord, etc.). As such, Primp Town is known to be located in France, making Puyo Puyo not a fantasy series, as France is just like that.
I was in a silly goofy mood and oops I started messing around with a Time Travel story because it's fun, Amitie has no idea who Clover is.
Ms. Accord & Popoi are the ones who instantly know what's going on, the second to catch on is Raffina(?
Sig just helps, he says that he doesn't have cousins, so she can't be related. Despite, ya know, the tiny bits of red in her hand, and similar ways to emote...