She was the first ship of the French Navy named in honour of Vice-admiral Suffren de Saint Tropez, who had died a hero of the American War of Independence on 8 December 1788.

[5] In December, she took part in the Croisière du Grand Hiver under Captain Pierre Augustin Moncousu;[6] upon departure, she broke her cables, but unlike the ill-fated Républicain, she managed to reach the open sea, followed by the frigate Vertu.

[15] In the night of 22 to 23 December, she accidentally collided with Nielly's flagship, the frigate Résolue, dismasting her of her bowsprit, foremast, and mizzen; only her mainmast stayed upright.

[18] In March 1802, the Redoutable was the flagship of a squadron of two ships of the line and four frigates under Admiral François Joseph Bouvet sent to reinforce Guadeloupe in 1802 and in the Saint-Domingue expedition in 1803,[1][19] departing on 9 January from Ajaccio with troops and arriving on 4 February.

[23][a] Redoutable was the third ship behind the flagship Bucentaure in the French line, coming behind Esprit-Tranquille Maistral's Neptune and José Quevedo's San Leandro.

When Neptune and San Leandro dropped behind Bucentaure, exposing her stern, Redoutable rushed to cover her and prevent Vice Admiral Horatio Nelson's Victory from cutting the Franco-Spanish line of battle.

[22] With her bowsprit almost touching Bucentaure's stern, Redoutable fired on Victory's rigging for ten minutes, trying to disable her to prevent the crossing of the French line, but did not manage to stop her advance, despite cutting off her foremast tops, her mizzen and her main topgallant,[24] and ended up running afoul of her.

A furious, fifteen-minute musket duel erupted between the two ships; the crew of Redoutable had been especially trained by Lucas for such an occasion,[25][b] and soon the heavy hand grenade and small-arms fire on Victory's quarterdeck mortally wounded Vice Admiral Nelson.

[22] Lucas later reported: A violent small-arms exchange ensued (...); our fire became so superior that within fifteen minutes, we had silenced that of Victory; (...) her castles were covered with dead and wounded, and admiral Nelson was killed by our gunfire.

Almost at once, the castles of the enemy ship were evacuated and Victory completely ceased fighting us; but boarding her proved difficult because (...) of her elevated third battery.

[28] After ascertaining that Redoutable was too damaged to survive the aftermath of the battle, and worried that she would sink before his wounded could be evacuated,[22] Lucas struck his colours at 2:30.

[31] The next day, Redoutable made distress signals, and Swiftsure launched boats to evacuate her passengers; she foundered around 7, taking 196 men with her.