It sounds like what is known as a Hippo, more or less. That's a formation that has the small center, the double fianchetto, and usually both knights developed toward the middle.
Thing about the Hippo, though, is that it's meant to be a counterattacking, reactionary defense, remaining flexible enough that you can absorb your opponent's attack, then react in a place where he's weakest.
If one attempts to play it as an attacking opening, one can run into real trouble. If you play aggressively in the center, somebody playing like this HAS to be too slow to organize an effective attack on your castled king. With control of the center, you can quickly and easily mobilize your pieces to back up your central attack. A direct assault on one side of the board from the formation you describe, executed that early in the game CAN'T possibly get his pieces coordinated to help in the attack before he gets steamrolled in the center.
Play for basic, fundamental opening principles. Take hold of the center, develp swiftly, and once done, determine to attack aggressively in the middle with central pawn pushes backed by heavy pieces and aggressive minor piece placements or even sacrifices.
You'll discover that opponents who waste time putzing on both sides of the board and THEN start willy-nilly with pawn moves early on get hopelessly behind and find themselves defenseless against a well-coordinated attack.
As a ~1100 blitz player, I often see other players push both center pawns one space and fianchetto both bishops. Then after I castle they push their pawns on that side to open up my king. I'm pretty sure this is a bad strategy as no grandmaster play like this, but I'm not sure exactly how to counter it. By the way, they often don't castle.