Born at Molsheim in Alsace, François-Joseph Westermann had served in the cavalry before becoming active in revolutionary politics. He played a prominent part in the insurrection of 10 August 1792, which led to the suspension of Louis XVI and the collapse of the constitutional monarchy, and subsequently served with Dumouriez in the northern armies. Arrested after Dumouriez's defection in April 1793, Westermann was cleared by the National Convention the following month and soon afterwards promoted to brigadier general and sent to the war in the Vendée.
An aggressive cavalry commander, he occupied Parthenay and penetrated as far as Châtillon during the Republican offensive of the summer of 1793, before suffering a serious reverse there in July. He later took part in the campaign north of the Loire and in the Republican defeat at Entrammes. During the final stages of the Virée de Galerne, his cavalry played a prominent role in the pursuit of the Vendéen army at Le Mans and Savenay.
Westermann's conduct and military record remained controversial, and after the campaign he was dismissed from command and returned to Paris. Pierre Philippeaux, who was engaged in a broader attack on the conduct of the war in the west, defended him publicly before the Convention in January 1794. Westermann continued to seek an explanation for his dismissal during the following weeks.
On 2 April 1794, after the trial of Danton, Desmoulins, Philippeaux and their co-defendants had already begun, Westermann was arrested following allegations arising from the investigation into Fabre d'Églantine. The Committee of Public Safety approved the warrant, and Westermann was subsequently joined to the same prosecution. He was condemned with Danton and the other defendants and executed on 5 April 1794.