I will be purchasing a Germany Rail Pass, and one of my routes is from Dijon, France to Basel, Switzerland. Can this count towards a day of travel towards my Germany rail pass?
Dijon to Basel doesn't go through Germany, so I don't see how it would count.
Alan, have you done the arithmetic to make sure that the German Pass makes the most sense? There are several people here who can help you get German tickets quite cheaply and you may find that the pass is way off cost effective. Back to your direct question, the Dijon (from Paris) TGV to Basel and onwards to Zurich never goes anywhere near Germany. Virtually all but the last km or two are in France only, with the last bit of the run into Basel SBB Hbf. How would you figure that a train which never goes near Germany would be able to be a German Pass day? The answer is "no".
I think maybe Alan wanted to make sure the ride from Dijon to Basel wasn't going to cost him any days off his German pass. As has been mentioned, he should investigate less costly options than getting a German Eurorail Pass.
For a good discussion of why passes are often a bad deal these days, here's The Man In Seat 61: http://tinyurl.com/bkw4u6c To find train routes in Europe, and find prices (full and discount) for trains that start or end in Germany, use Bahn (German rail), following Rick's tutorial: http://www.ricksteves.com/plan/tips/db_tips.htm To investigate prices on French trains, use http://en.voyages-sncf.com/en/, and choose "France" as your ticket collection country.