Louis XVIII (1785 - 1840?), known as Louis-Charles, was King of France in the 1820s. Although Sobel does not specifically say so, it is likely that he was the younger brother of Louis Joseph, who became King Louis XVII in 1793, and that he succeeded as King of France after his brother's death in the early 19th century. Sobel mentions that Louis XVIII was strongly anti-British, which was to be expected of someone who grew up seeing Paris occupied for several years by British troops, and his royal brother reduced to a British puppet.
Louis' anti-British feelings led him to make common cause with Mexican President Andrew Jackson, whose own hatred of the British was well-known. In February 1824 it was revealed that Louis' government had agreed to loan $4 million to the Mexican government, with more to come later on.
Sobel makes no further mention of Louis XVIII after the 1820s. By 1845 he had been succeeded on the French throne by Henry V.
Sobel's source for Louis XVIII and his alliance with Jackson is Henri de Amory's The Ghost of Lafayette: The Franco-Mexican Alliance (Mexico City, 1959).
IOW Louis-Charles outlived his older brother Louis Joseph and became the presumptive King of France after his father's execution in 1793. He was never crowned and never reigned, but French royalists refer to him as Louis XVII. Louis-Charles died in captivity in 1795, after which his uncle the Count of Provence claimed the throne as Louis XVIII.