Well, I am sure Bennison's the one you tried as they sell at the Green City Market. They are indeed excellent breads, and perhaps worth the schlep to Evanston (if buying at the twice weekly Green City Market will not do). Green Grocer also sells Bennison's bread if you can get to that hood. Still, if you are looking for a place in the city, Fox & Obel is just as good, if not better in certain catagories. F&O's sourdough miche is the best bread, I believe, in the city. Medici, in Hyde Park is about in the same catagory, although I believe not quite. Red Hen would be a small step down again, but all of these are very good breads.
As LAZ sez, the city is filled with very good Eastern European style breads if that is what you mean, but for French style bread, any of the above will do ya good.
Think Yiddish, Dress British - Advice of Evil Ronnie to me.