Those are the lands around Avignon, still belonging to the Pope (until the French Revolution).

From 1309 to 1377, seven successive Popes based themselves in Avignon, rather than Rome. (This period was sometimes referred to by its opponents as "The Babylonian Captivity".)

Even after 1377, when the "legitimate Papacy" returned to Rome, there were still "Anti-Popes" ruling from Avignon until 1403.

Before the Popes moved to Avignon, they had acquired land in the area. The Comtat Venaissin comprised a large section of land between the Rhone, the Durance, and Mt. Ventoux. It surrounded the city of Avignon, and the Principality of Orange. It was part of the Holy Roman Empire, until Alphonse, Count of Poitiers, bequeathed it to the Holy See on his death in 1271.

Papal ownership of the Comtat was probably one of the reasons the Popes moved to Avignon, when they wanted to get out of Rome. The Popes did not own the city of Avignon, however, until 1348, when the Popes bought it from Joanna I, Queen of Naples and Countess of Provence.

By 1789, the French border had moved Eastwards, at the expense of the Holy Roman Empire, so the Papal estates of the Comtat and Avignon were surrounded by France.

Nonetheless, they did not belong to France, and were still Papal lands until 1791, when the French organized a plebiscite and annexed them. This was not recognized by the Papacy until 1814.

It is the Comtat Venaissin, which is around the modern day city of Avignon. It was purchased by the Papal States in the 11th century, and annexed or reincorporated back into France by a plebiscite during the French Revolution, sometime after 1789. I don't recall the exact year.