I don't see how you could possibly walk to the Four Points from either station. The Tram (81) to Richmond can be accessed at Gare du Midi and it will take you to the Bially(?) stop right at Avenue Louise. It's maybe a 15 minute tram ride and stops less than a block from the hotel.

I just spent four days at the 4Pts and couldn't be more pleased. I had a gigantic room with a huge bathroom and the service was very good. It is a 4Pts, but for the price it seemed like a good deal.