To "push" or pousser often occurs as a technical term in medieval accounts of combats written in French. What seems to distinguish a "push" from other thrusts is that it's expected to include a lot of momentum transfer, and to knock the target back or down if everything goes right. This would be in contrast to a jab or rapid pool-cue pop.
When Galiot de Baltasin and Phillipe de Ternant fought on foot with lances in 1446 they did each of their pushes with the lance with a run-up of seven paces on each side:
And they came to meet each other with a push of the lance, so harshly that the stroke from Galiot broke the point of his lance, a good half finger width, and lord de Ternant hit Galiot on the edge of his bassinet, and broke clear through it. The lord de Ternant took a step in completing the blow, and as he gave the blow he drove his foot nearly a foot deep into the sand.
la Marche, Olivier de , Mémoires Paris 1884 II. 70-72 Translation copyright 2006 Will McLean
At Vannes in 1381 Clarins, a bastard of Savoy, struck his opponent, Edward Beauchamp, to the ground twice with his spear.
Then came the last, Edward Beauchamp and Clarins de Savoye. This bastard was a tough and brave squire, and as well formed in all his limbs as the Englishman was not. They ran at each other with a hearty good will: both set their spears on their breast in pushing; so that Edward was struck down and backwards, which angered the English greatly. When he was raised up, he took his spear and went against Clarins and Clarins against him, but the Savoyard again struck him to the ground, which made the English very angry: they said, Edward is too weak against this squire, and the devil was in him to joust against the Savorard. He was carried off among them, and said he would fight no more.
Froissart, Jean, 1867-1877 Oeuvres ed. Kervyn de Lettenhove, Brussels Vol. 9 pp. 326-327 Translation copyright Will McLean 2012
Similarly, at Noseroy in 1519 "one of the men of arms of the sustainers, named Jean de Chantrans was carried to the ground by a stroke of the large end of the lance, by Claude de Bussy, lord de Vescles."