Count Clerfayt's army had been retreating for months. After the catastrophe at Fleurus in late June, the Austrians had given up the Netherlands and fallen back across the Meuse, then across the Ourthe, then finally to the Roer, a sharp-banked tributary running roughly north to south between Roermond and Duren. It was the last river before the Rhine itself. Clerfayt did what he could. Bridges were destroyed, fords were dug up so cavalry could not cross, and the steep banks were entrenched along sixty miles of front. The river ran high that autumn, deepening the defense. He placed the bulk of his 76,000 men between Duren and Linnich, with an advanced position west of the river at Aldenhoven, in front of his headquarters at Julich. On paper it was a serious line. In practice, Jourdan was bringing more than 100,000 men against it.

Kleber moved first, on the French left, in darkness. His infantry pushed Franz von Werneck's light troops back from the west bank with sustained artillery, then a remarkable thing happened. Jean-Baptiste Bernadotte, the future king of Sweden, took the 71st Demi-Brigade and four grenadier companies and simply swam the river south of Ratheim. The future Marshal Ney crossed with the cavalry behind him and led a regiment in a charge on the far bank. It was the kind of small, audacious action that Revolutionary France was producing again and again in those years, careers being made and futures rewritten in a few minutes of icy water and gunpowder. Kleber's other divisions could not get across that day, but Bernadotte's bridgehead held.

In the center, Jourdan watched his plan unfold. Francois Lefebvre's division advanced in lines of battalion columns and took Linnich on the left. Jacques-Maurice Hatry took Altorp on the right. Between them, the divisions of Jean-Etienne Championnet and Antoine Morlot pushed up onto the broken ground in front of Aldenhoven. Championnet later wrote that he could use the rolling terrain to bring light artillery and infantry columns close to the Austrian positions before the enemy could see them clearly. The town fell. The Austrians pulled back to prepared works east of Aldenhoven and held there until they realized that French troops on both flanks were threatening to cut them off. Then they retreated across the river toward Julich. On the French right, Francois Severin Marceau pushed his division across the Roer by three in the afternoon and took Duren by nightfall.

Jourdan expected to renew the assault the next morning. Clerfayt did not give him the chance. With his river line breached on both flanks and his army outnumbered, the Austrian commander withdrew under cover of darkness and never stopped until he was across the Rhine at Cologne on 6 October. The same day, French troops walked into the part of Cologne that lies on the west bank. Within three weeks, Jourdan held Bonn, Krefeld, Kleve, and Koblenz. Dusseldorf fell after a bombardment on 23 October. Maastricht, besieged by Philibert Duhesme, surrendered on 4 November once Kleber's siege guns were in position. The campaign that began with the dawn crossing at Ratheim ended with France holding the entire west bank of the Rhine, a strategic prize that would shape the next twenty years of European war.

Aldenhoven itself is a quiet North Rhine-Westphalian town today, the Roer a manageable river crossed by ordinary bridges. The battle barely features in popular memory of the Revolutionary Wars, overshadowed by Fleurus, Marengo, Austerlitz. But the men who fought here would be remembered. Bernadotte became Marshal of France and then King of Sweden, founder of a dynasty that still reigns. Ney became Napoleon's most celebrated cavalry commander, the bravest of the brave, executed by firing squad after Waterloo. Lefebvre became Duke of Danzig. Marceau, only twenty-five at Aldenhoven, would be killed in action two years later. Jourdan himself became a marshal under the Empire. The Battle of Aldenhoven is inscribed on the Arc de Triomphe, one stone among hundreds, marking the day a generation of soldiers walked across a river and into history.