I have never been to Moulin Rouge but I found this tour on the web site. It is the 10th one down. I think this company was one of the ones recommended on this site.
The advantage of a tour is central paris pick up and then pick up
at the Moulin Rouge after the show. For the money you get a tour of the city at night as well as the show.
http://paristours.france.com/paris-nigh ... p?hotelid=
I have not found any tours which include dinner if you wanted to go that route.
i do know if the seats are better with dinner rather than just going for the show and champagne or wine.