Not a good option as you definitely need some sort of personal transport, especially for a day-trip. Check car rentals or a private guide with provided car.
I would like to visit the Verdun battlefield in June, 2015, possibly on a Sunday. I do not plan to rent a car. Can you recommend any buses (e.g., the open bus tour or the French guided bus tour, etc.) that can take me from the City of Verdun (or Reims) to the Verdun battlefiled? How about for a reasonable cost (e.g., under 100 euros pp)? Also, do any tour buses work on Sunday?