The Varenne (French pronunciation: [vaʁɛn] ⓘ) is a river of Normandy, France, 39 kilometres (24 mi) in length, flowing through the department of Seine-Maritime.

[1] The river is the ultimate source of the surname and given name Warren, via William de Warenne of Bellencombre castle, his hereditary seat.

de Warenne was a companion of William the Conqueror and made first Earl of Surrey in 1088 as reward for his service during the Norman Conquest.

Of the three rivers that form the Arques, the Varenne is the shortest but paradoxically has the largest catchment area and highest speed (3.5 m/s).

Its course takes it past the communes of Saint-Martin-Osmonville, Saint-Saëns, through the forest of Eawy and on to Bellencombre, Saint-Hellier, Torcy-le-Grand, Torcy-le-Petit, Martigny, and finally Arques-la-Bataille where it joins the rivers Eaulne and Béthune to form the Arques.