Neoclassicism
The rise of the Neoclassical period occurred before the French Revolution started. However, it is commonly associated with the revolution because the style of the art in that time represented what the rebels believed in: purity and liberty. Before and during the revolution, painters such as Jaques-Louis David and Jean-Francois Pierre Peyron became more interested in painting actual events versus what people wanted to happen. They took inspiration from the moral values of the Romans and the ideas of simplicity, austerity, heroism, and stoic virtue. Artists in this period took great value in details and accuracy in their paintings. It was also considered a reaction to the frivolously decorative Rococo style of art. This period lasted from 1750 to 1850.
Romanticism
The rise of the Romantic period occurred as a reaction to the Industrial Revolution and the Age of Enlightenment. The themes of this period are more emotional with spiritual freedom, individual creative expression and nature being paramount . This is because the advancements in science were very logical and rational, so as a backlash, the period was more idealistic than realistic. This is best summed up by the painter, Caspar David Friedrich, who said, "The artist's feeling is his law." This shows that they were revolting against the order of mankind and instead letting their art flow freely from their imaginations. This period lasted from 1780 to 1850.
Random fun fact: it was during this time period in which the British started their tradition of drinking tea in the afternoon.