Look at Homeaway.com.
Have you tried the 'Location Meublée ' option on that Moustiers site. There seem to be several furnished apartments but whether they will rent for 2 days is another matter.
Most short-term rentals are going to require more than a 2-night stay. Have you tried Airbnb?
Moustiers is a small place, I’m pretty sure. That your options are going to be limited.