The first part of our trip begins in France and only requires two days of second class train travel (Chamonix to Beaune and Beaune to Zermatt). The rest of the trip will be in Switzerland - much of it in Zermatt and Wengen using the private rail lines. I am thinking of paying for the France portion of the trip and getting a Swiss Pass for the remainder of the trip so we can utilize the 50% discount on the private rail lines. Would this be the most economical?
The France-Switzerland passes do not work well in Switzerland for several reasons. For one, as you already know, they do not fully cover some of the private rail lines; you have to pay a supplement. For the mountain trains and lifts, the 2-country pass may cover only 25%. Also, they are only available in First Class, which you don't need in Switzerland, and often isn't available on the mountain trains.
So I think you would be better off with some kind of Swiss pass, and paying for your France travel separately.
BTW, if you could reverse the order of visiting, a journey from Chamonix into Switzerland is covered with a Swiss pass---so it would cover from Chamonix to Zermatt. See the coverage on the Swiss Travel System synoptic map:
http://rail.myswitzerland.com/download_sts/uebersichtskarte_en.pdf
Note that a regional pass like the Berner Oberland pass suggested above won't help you in Zermatt. A Swiss Pass or Flex pass, in Saver version if there are 2 or more of you, is probably the one you want. This will cover your travel to Zermatt and the lifts and trains up from th evalley (like Gornergrat, Sunnegga, etc.) at 50%.
Having done a similar trip in reverse, get a Swiss pass and do point-to-point tickets in France. The Swiss Pass is one of the few rail passes that is truly worth it and you may be pleasantly surprised when you go to purchase your p2p tickets in France. We actually got a really good special deal to go from Basel to Strasbourg just walking up to the ticket counter that day.