I've already written about Dijon, Beaune and Burgundy, all quickly accessible from Paris (about 1-1/2 hours) on the TGV. You can actually go to the real south of France in less than 2-1/2 hours. I'm posting a few photos of Avignon, where I've spent substantial research time. Avignon is one of the remaining walled cities from the Middle Ages, and the papal palace, where the popes lived during the Avignon papacy during 70 years in the 14th C., takes up most of the city (a very cultural place with great restaurants, music, film festivals, etc.) as you can see in the first photo taken from the Pont d'Avignon, famous for its children's song dating from the time of the Plague: Sur le pont d'Avignon, on y dance, on y danse... The Petit Pont leads over to Villeneuve-lez-Avignon. It was part of France in the 14th C., whereas Avignon was owned by Queen Joanna of Naples till she sold it to the pope to be absolved of the gruesome murder of her husband at the time of the plague. It used to be thought the Kings of France orchestrated the Avignon Papacy but that has been shown to be false, except for its first pope, Clement V, who took over there after the whole papal curia escaped to Avignon following the shenanigans of Pope Boniface VIII. He had forced his predecessor, a monkish sort named Celestine V who had never wanted to be pope, to abdicate and then probably murdered him. Boniface was a jerk, and Dante, a contemporary, placed him in Inferno. His high-handed actions of claiming papal supremacy over all of Europe led to his papal palace near Rome being sacked and burned and he died a few months later. The courtiers (and popes) chose not to stay in the volatile environment of Rome, and escaped to the papal enclave, which then turned from a town of maybe 20,000 people to a major place because that's where poets and artists came for patronage.
The second is part of the Papal Palace, which is huge, and started in the 1320s. I got to visit what is called the "Palais Secret" (Secret Palace), not because it is truly secret, but because it is closed to the public except for tours in France. Since I'm doing a book on Avignon, I got in on it, and it takes you through the oldest parts of the palace (with no elevators, no restrooms, but remains of the papal latrines and gyms. The roof showing the angel was taken from one of the highest points. Then a short trip away is the Pont-du-Gard, the Roman Aqueduct, and the town of Châteauneuf-du-Pape, home of my favorite wines in the world (which you can also buy in the papal palace gift shop.