tournament

Tournament comes from Old French tornoiement (which survives in Modern French as tournoiement), itself formed from the verb tornoier.

The facts available don't trace a documented shift in meaning beyond this French source, so the honest story stops there: it entered English from that Old French noun.

Tornoiement is built on the verb tornoier, so the two are directly linked in French, though no further English cognate is given in the facts.