Does anyone know where you can store baggage for about a week or so? I know there are places mainly in Paris but I'm looking for somewhere in southern France, Germany, or northern Italy. Thanks!
A lot, but not all, train stations in Germany have luggage lockers, but I think they can only be used for a few days. Some of the real major stations have long term luggage check rooms, Gepäck Aufbewahrung.
Munich does. See here. This webpage is in English, but I don't think it has been updated in a long time. They give the price as €2,05 (the equivalent of DM 4,00). The German language side says the price is €5,00 per piece per day.
Apparently Munich also has long term lockers for a minimum of €30 (small), €45 (medium), and €60 (large). That would give you a months rental, but I assume you could take your stuff out sooner.
If you might be staying overnight in the same place on each end of the week, you might inquire if the hotel could keep your baggage for you. Most smaller family run places have someplace to stash a bag or two, I have done it frequently for a morning or afternoon, but I am sure that longer term could be arranged.