The Loire Valley
Only a short train ride from Paris, the Loire Valley makes for a wonderful escape from the city. Full of castles, vineyards, roads to bike, and foods to try, the Loire Valley is the perfect addition to your trip - whether for just a one-day escape or for an extension on your Paris trip.
While I wouldn't necessarily recommend attempting to see the Loire Valley in a just one day, if short on time and desperate to see some of this famous region full of chateaux (which is actually not too far from the city), then know that it is extremely accessible. From Paris you can train to Tours in approximately just one hour. Tours itself is a lovely town, full of charm, timbered buildings, a great market, and some delicious restaurants where you can taste local wines. From Tours, the rest of the Loire Valley is quite accessible. Or perhaps you'd like to go straight to Orleans or Amboise - both possible as well.
If only going for a day, it's best to know what you're going for and plan accordingly. Do you want wine tours or castles? Quaint towns or palaces surrounded by fields? Perhaps you're looking to bike the Loire Valley, which is quite common as well. There is plenty to see and do, and if only venturing there for a day it's best to know what your priorities are and try and choose a starting point that's not too far away by train, such as the town Tours. It may also be worth considering booking a tour for the day, either one that starts in Paris or in one of the bigger cities/towns in the Loire, this way you may be able to see more in one day without worrying about transportation.
Again, while it is definitely possible to make a day-trip out of it, I highly recommend you reconsider and spend at least a couple of days in this region, so as to best experience it and not feel rushed or cheated.
A few of the most popular castles to visit in the region include: