The car was built at Matra's Formula One base at Vélizy-Villacoublay in the southwestern suburbs of Paris, designed under the direction of Gérard Ducarouge and Bernard Boyer.

Jackie Stewart got to test the Matra V12, but since a large part of the Tyrrell budget was provided by Ford, and another significant sponsor was French state-owned petroleum company Elf, which had an agreement with Renault that precluded supporting a Simca partner, the partnership between Matra and Tyrrell ended.

The South African Grand Prix was good for Beltoise with a fourth-place finish while Pescarolo had a disappointing seventh place.

[6] Next, the British Grand Prix was a bad race with both retiring, Beltoise with a wheel problem and Pescarolo with an accident.

[11] Then the United States Grand Prix saw Pescarolo in eighth place, but Beltoise retire with a bad handling car.

[12] Finally, it was the Mexican Grand Prix with Beltoise fifth and Pescarolo ninth, although the race was delayed by an hour because of crowd control.

[25] More gearbox problems followed at the Spanish Grand Prix,[26] before luck came Amon's way with two sixth-place finishes at Monaco[27] and in Belgium.

[28] The French Grand Prix saw Amon on pole and he was leading the race until a puncture forced him to pit, but he charged back through the field, bettering the Charade Circuit lap record to finish third.