Why do you think the French laid claim to land beyond the St. Lawrence River

Because it was kind of a water crises but because of enviormen produc such as gold and more

The answer is: Because they had already verified that it was not possible to navigate it through its flow.

Explanation:

In the Iroquois village of Stadacona, Cartier met again with Chief Donnacona, who tried to dissuade the French from continuing to climb the river, since he wanted to preserve the monopoly of river commerce. Cartier did not accept, released his two children and decided to continue without guides or interpreters.

The flow of the river soon prevented him from continuing beyond Lake Saint-Pierre.

The answer is: Because they had already verified that it was not possible to navigate it through its flow.