So far we know the first Gym Leader specialises in Bug-type Pokémon. The second, third, and fourth will most likely specialise in Rock-types, Electric-types, and Fighting-types, respectively.
I would think having a Grass-type starter would make the first Gym Leader difficult to beat. Fennekin might have trouble with a Rock-type, however. Grass-type Chespin should do fine against Rock-types and Electric-types, but like I said it will have some trouble at the first Gym. If it evolves into a Dark-type before the fourth Gym it might have a challenge there too.
Froakie will have problems with the Electric-type Pokémon from the third Gym, but should do fine in the other Gyms.