You didn't say if you have already seen the Loire, or Normandy, or the Channel Islands, or near-Paris outings like Giverny and Chartres and Rouen. I presume you've been to Paris. If you are afraid of too much France, consider going to the near corner of Belgium, which would get you the very popular destination of Bruges (via Louvre-Lens?). Gent and Antwerp are very affordable, and you can fly home from Brussels if your air fare cooperates.
It would be helpful to know if "seniors on a budget" means "trains only". For example, Brittany and Normandy are loaded with lovely private gardens that could be beautiful by the middle of May, but hard to see without a car. Many people with cars want to see medieval village remains and neolithic (?) stone monuments near the coast, but I haven't been that far into Brittany. Luxembourg has a cheap airline, and you could hit Trier, Germany