I believe that if you use "soft wheat" flour (I think there's a brand called Lily) as opposed to "hard wheat" flour (like Gold Medal) you'll get a softer fluffier "crumb" (the internal soft part) in the bread.
For the record, I believe that soft wheat flour has less gluten than hard wheat flour. Gluten is what binds the flour together and produces a firmer loaf, so adding it to flour would be going in the opposite direction of where you say you want to head.
You say that you want the soft crumb like Italian or French bread, which is a bit confusing to me, because standard French bread (i.e. a baguette) has what I would call a chewy consistency inside. For that type of bread, you'll need flour with a high protein content and made from hard wheat. King Arthur Flour makes "French Style" bread flour, sold on-line at Amazon or through The Baker's Catalogue.
Hope this helps.