In 1770, at age seventeen, Giroust started studying painting in the studio of Joseph-Marie Vien, a pioneer of Neoclassicism.
In 1775, Vien left Paris as he became director of the French Academy in Rome, and took David with him.
Giroust thus decided to move to study with Nicolas Bernard Lépicié.
Once back in France, Giroust was elected at the Academy, on 29 March 1788, with the painting Oedipus at Colonus, a work of pure Neoclassicism.
He didn't champion the new regime, and eventually retired to the countryside and hardly painted anymore.