The Trois Pointes river originates on the Canadian Shield, at a small unidentified lake (length: 0.24 km (0.15 mi); altitude: 441 m (1,447 ft)).

The mouth (south side) of this small forest lake is located 9.0 km (5.6 mi) northeast of the confluence of the Françoise river and the rivière aux Anglais, at 0.8 km (0.50 mi) south-west of a bay in Lake Franquelin and 35.2 km (21.9 mi) north-west of the confluence of the rivière aux Anglais and Baie des Anglais on the north shore of the Gulf of St. Lawrence.

From the head lake, the course of the Trois Pointes river descends on 11.9 km (7.4 mi) entirely in the forest zone, with a drop of 195 m (640 ft), according to the following segments: The Trois Pointes river flows on the north bank of the Lac La Chesnaye, which is crossed to the northeast by the current of the rivière aux Anglais, in the unorganized territory of Rivière-aux-Outardes.

From the mouth of Lac La Chesnaye, the current descends the course of the English River for 11.2 km (7.0 mi) to the Baie des Anglais, located on the north shore of the Gulf of Saint Lawrence.

The toponym "Trois Pointes River" was formalized on August 2, 1974, at the Place Names Bank of the Commission de toponymie du Québec.