The strength of the Euro will make perhaps the biggest difference to foreign visitors, but even then the Dordogne is, by regional and global standards, not particularly expensive. Expect to pay much the same than you would elsewhere and certainly less than you would pay in Provence for example.
What you can expect is value for money wherever you go. For food shopping try the local outdoor market, held daily in the big cities and weekly in small towns and villages. These are not necessarily cheaper than shops but the produce is guaranteed to be local and fresh.
For really low prices on a whole range of goods try the local Hypermarché. These are huge retail outlets, usually to be found on the outskirts of town, which sell everything from food to clothes. Hypermarchés to look out for are Carrefour, Leclerc, Auchan, Intermarché Hyper and Géant Casino.