I'm not familiar with using the European train transportation websites yet to check if my husband and I can get from Paris to Arbois just using our Eurail passes. I have one of Rick's travel maps showing train routes, but it doesn't have Arbois on the map. Any guidance? Thanks!
Check out the French national railway website at http://www.voyages-sncf.com (little Union Jack at bottom left for English). That'll give you the schedules. You appear to go to Mouchard, then take a 10 minute bus ride. Don't forget, you must make and pay for reservations, and pay an extra supplement, for fast trains like the TGV, even with your pass, and those are difficult to arrange from here. If you haven't yet purchased your Eurail passes, you might want to check point to point ticket prices for the journeys you plan, to see if you might end up spending less money, and undergoing less hassle, than with a pass. Search recent days' postings for the experiences of a family trying to get from Milan to Paris with Eurail passes, but without advance reservations. Reservations on any European train for Eurail holders are very limited.
You can also check the Rail Europe website. It has been many years since I've taken the train to Arbois, but when I did, the train was not a part of the national railway system, but a little commuter train that wasn't included on my Eurail pass. If you haven't been to Arbois, don't let the transportation handles keep you from going. It is such a lovely town. If you have time, do a wine tasting at Henri Maire - the "vin fou" is great!