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The son of a notary, intendant to the prince de Rache, avocat to the parliament of 1789, companion and collaborator of Saint-Just, Le Bas was elected député to the National Convention for the Pas-de-Calais in 1792, sitting among the Montagnards. A discreet, cold, and loyal representative, he voted for King Louis XVI's death and against the sentence at his trial (i.e., against the people's appeal). Le Bas and Duquesnoy were delegated to the armée du Nord in August 1793, and Le Bas proceeded with the arrest of generals Richardot and O'Moran for inability. A member of the Committee of General Security, he was among those close to Robespierre, Couthon, and Saint-Just, who had a brief and discreet relation with his sister Henriette.
He and Saint-Just were made the Convention's commissioners to the armies and set out on this mission to eastern France, where he reorganised the army after its reverses at Wissembourg. Saint-Just and Le Bas were also later sent to reorganise the armée du Nord by the Committee of Public Safety in the face of an attempted return by Austrian forces after Wattignies - it was this reorganisation that made possible the victory at Fleurus.
Faithful to Robespierre to the bloody end on 9 Thermidor, when Augustin Robespierre demanded that he share his brother's fate, Le Bas demanded that he share the fate of Saint-Just, committing suicide by pistol just as the anti-Robespierristes under Barras and Léonard Bourdon broke into the Hôtel de Ville (where Le Bas had taken refuge with Maximilien Robespierre, Augustin Robespierre, St-Just and Couthon).
He married Elisabeth Duplay, daughter of Maurice Duplay, Robespierre's landlord in Paris, and their son was Philippe Le Bas (1794–1860), who would be Louis-Napoléon Bonaparte's preceptor until 1827 then director of the library of the Sorbonne (from 1844 to 1860), a member of the Académie des Inscriptions et Belles-Lettres (1838–60) and president of the Institut de France (from 1858).