He was the son of the miniaturist François-Elie Vincent and studied under Joseph-Marie Vien. He travelled to Rome, where he won the Prix de Rome in 1768. From 1771 to 1775 he studied there at the Académie de France.
In 1790, Vincent was appointed master of drawings to Louis XVI of France, and in 1792 he became a professor at the Académie royale de peinture et de sculpture in Paris. In 1800, he married the painter Adélaïde Labille-Guiard.
He was a leader of the neoclassical and historical movement in French art, along with his rival Jacques-Louis David, another pupil of Vien. He was influenced by the art of classical antiquity, by the masters of the Italian High Renaissance, especially Raphael, and among his contemporaries, Jean-Honoré Fragonard.
He was one of the founder members of the Académie des beaux-arts — part of the Institut de France and the successor to the Académie royale — in 1795. Towards the end of his life he painted less due to ill health, but he continued to receive official honours.
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