France or Switzerland?

France for sure. Just a short hop by train to Sarlat from Bordeaux and the Dordogne region.

I would stay in France and save Switzerland for another time.

Yes, France for sure. If you're going from Bordeaux and have a car, you might want to try Gascony (Gers and/or Lot et Garronne departments). Fources, Montreal du Gers, Nerac, are all interesting towns/villages. If you're going from Paris, consider the Loire Valley: Amboise, Chinon, Blois area.

I'm most familiar with Switzerland, but I don't know why you'd head over there for a few days when there's plenty to appreciate closer to the region where you'll already be based. Keep it simple. : )

Wow, I would totally go to Switzerland over France any day of the week... but thats just me.

With only three days I think Switzerland is just out. The Dordogne is a great suggestion if it fits with your itinerary.

Another plus for staying in France (which I love)... it's a lot less expensive than Switzerland.

You could easily spend the three days in Paris, but based upon your preferences, the Dordogne is the region you want. My wife and I were there for just a couple of days in 2003 and hope to go back. Depending upon logistics, Normandy is also very nice.

Annecy is a beautiful town in the Rhone-Alpes region of France which gives you a taste of Switzerland. It is on the banks of lake Annecy and it is a really lovely setting.
I'm tending towards Switzerland though. Oh dear, you're going to end up with so many different opinions. Perhaps stay in France as you have not been before and there is a lot to see. I'm off, my bum's getting numb sitting on this fence.