Political events produced an interlude in Français' career. The French Revolution of 1789 had not gained universal support and there were attempted counter-revolutions in parts of France. In the Vendée region in the west of France there was an uprising which was sparked off by the introduction of conscription in February 1793. By the middle of March there was an alliance of Royalists and peasants with a fair size army. Français joined the government army in May 1793 which was moving to put down the rebellion.
The rebel army at this stage numbered around 30 000 and they took the towns of Thouars, Parthenay, and Fontenay in May. Crossing the Loire the rebels moved east taking Angers in the middle of June but their progress was stopped when they failed to take the town of Nantes. During the summer months there was confused fighting with the government forces somewhat fragmented. Français continued to fight with the government forces and as the autumn approached they became a more cohesive force under a single command and heavily defeated the rebel army (by this time numbering around 65000) in October.
The fighting did not stop there and it was not until the end of December that the government forces mopped up all resistance. Français, however, left the government army in October and returned to teaching. The period of army life must have been attractive to Français for he quickly rejoined the army as an officer and served for a further four years until October 1797 when he was appointed professor of mathematics at the École Centrale du Haut-Rhin in Colmar.
Français never seemed to be one to stay in any one post for long but this appointment in Colmar lasted longer than any of his others. He remained there for six years but, once he moved on in September 1803 to the Lycée in Mainz, he was to teach mathematics in a number of different institutions over the next few years. In 1804 he taught at the École d'Artillierie in La Fère, then he returned to Mainz and taught at the École d'Artillierie there.
Much of François Français's work was published after his death by his brother who added to it in a way to make the contribution of each hard to distinguish. François worked on partial differential equations and his memoir of 1795 on this topic was developed further and presented to the Académie des Sciences in 1797. Lacroix praised Français' work and described it as making a major contribution to the study of partial differential equations; however, it was not published.
Français was friendly with Arbogast and together they worked on the calculus of derivations. After Arbogast died in 1803, Français inherited his mathematical papers and continued to work on the calculus of derivations. He presented a memoir on this topic, in particular applying the methods to study projectiles in a resistant medium, to the Académie des Sciences in 1804. This memoir was very highly praised by Biot in a report of 22 April 1805, but again the work was not published.
After this Français did work which was praised by Legendre, Lagrange, Lacroix and Biot but submitted no further memoirs during his lifetime. However, as described above, his brother published much of his work after his death, publishing four memoirs of François Français's work. Taton, writes in :-
While not of the first rank, the mathematical activity of the Français brothers merits mention for its originality and diversity.
Article by: J J O'Connor and E F Robertson