Why did Cartier sail down the St Lawrence River?

Jacques Cartier sailed up the St Lawrence River, as far as the Lachine Rapids, in search of a route to Asia. When he found that the route was impassable, he then turned around sailed back down the St Lawrence.

The concepts of "up" and "down" a river relate to the flow of the water, not a direction on a map. Travelling up a river means travelling against the flow. Travelling down a river means travelling with the flow.