The Refugio Elena is up the road from La Palud. Then there's a climb to the Col Ferret.
I spent the night at the Col de Fenestre Hotel in Ferret. You have to buy tokens for the shower. I should have bought two or three instead of one, because the water ran out when I was still soaped up. The view was wonderful (below).
The trail from here to Champex is mostly through the woods, without the beautiful views I've had so far. One interesting thing was a bunker off by the side of the trail. At Champex I stayed in the Chalet en Plein Air. That was my least favorite place. The food was mediocre, the people not very friendly. This is a fairly large town, so maybe there's another place to stay.
A novel water fountain.
Next: Champex to Chamonix