I make brie all the time... and you should probably do this, it's one of the easiest cheeses to do..... check pictures at my blog: http://knowwhey.blogspot.com/2009/10/why-not-camembert.html
You can make much better brie than you can buy, if you can get some high-quality milk.
However, you *could* ripen many store-bought bries, because mostly they are not dead. I can't speak for some of the worst ones, which possibly have been neutralized somehow. But, the point about brie (same as camembert), is that it is a surface-ripened cheese; the white mold on the outside is actually responsible for the flavor, texture, and progressive softening of the curd.
Also, I have many times cut a small piece out of a wheel, and then put it back in the box to continue ripening. It doesn't stop, because it ripens from the Outside In. (I ripen them in plastic food storage boxes, the kind with a little hole in the lid, for keeping lettuce or vegetables in the fridge).
I ripen at cave temp, which is around 52 degrees. Any warmer than that, and the pace of ripening is uneven with a series of possible undesirable results. Colder than that, and ripening is slowed, and eventually the cheese will get dried out...
So if you had a French brie, you could ripen it further, I'd say.
Sue in VT.