Hi
We've just recently moved to Lausanne. I've found a health-food store named Dumas that has a fairly large range of gluten free foods (pasta's, breads, cakes and crisp-breads etc). Our local Manor store stocks pasta and flour. Finally our local pharmacy stocks pizza bases and breads.
I'm sorry this is not Basel specific. I'm hoping the information may cross-pollenate and that there are stores in Basel as well as Lausanne .