Chespin's first move is pretty obviously Solar Beam, and the second one was Shadow Claw (I think). It's a cross between a Chestnut and a Porcupine (Ches + Pin), further supported since the French name (Marisson) which is a mix of Marron (chestnut) and Herisson (hedgehog). I think it'll evolve into a Grass/Ground, something like Sandslash without a Water weakness.
The Fire starter, Fennekin, is based on, obviously, a fennec fox, a nocturnal desert fox. It's using Ember and some other move (Confusion?). I'm really not sure what it's final typing will be, since the likely ones all already exist (Fire/Ground, Fire/Psychic, Fire/Dark, Fire/Fighting because,you know).
The Water starter is a cat. If we're lucky, it won't evolve into Politoed. From the name, it *might* be a mix of Frog + Foam + Rookie (the French (Grenousse) might be Grenouille (Frog) + Mousse (Foam or Lather)) which doesn't tell much. It might be Water/Poison. It's pretty much guaranteed to get Bubble and Bubblebeam too, if my interpretation is right.
Y-Bird, I think, is part flying because, if you stop the vid at 0:56 and at 0:57 (double click the play button to see it slowly), there's a beak. The claws and stuff make me think Dark type (the head crest reminds me of Absol, for example), but it could really be anything.
X-Deer is, as the offspring of Virizion and Dialga, Steel/Dragon/Grass/Fighting/Psychic/Something.
Of interest is the link between the game titles and the chromosomes (X/Y, determining gender), so that we may have the first title legends with a gender (Male for Y-Bird, Female for X-Deer).
L'ennui est ma Muse.