Final answer:
France challenged Spain's territorial claims in the 1600s by exploring areas of present-day Texas, amidst centuries of imperial rivalry and economic ambitions in North America.
Step-by-step explanation:
During the 1600s, France challenged Spain's territorial claims by exploring the region that includes present-day Texas. After the Treaty of Tordesillas initially carved the non-European world between Spain and Portugal, other nations like France and the Netherlands sought economic interests in the Americas.
France, in particular, focused on the fur trade in North America, which was not just an economic endeavor but also a strategic move to contest Spanish power. Their territorial ambitions in North America, and specifically, the interest in a region like Texas, which was part of Spanish America, exemplified the complicated relationships and rivalries that emerged among European powers during the era of colonial expansion.
French incursions into territories that were formally claimed by Spain were part of larger efforts to weaken the Iberian dominance in the New World. Although Spain managed to maintain its vast American empire for some time, the actions of the French, along with other European powers, signaled the beginning of the end for Spanish hegemony in the region. These early explorations and settlements by France set the stage for future geopolitical changes, as evidenced in the subsequent history of Texas and its eventual drift towards American influence and control.