Giovanni da Verrazzano’s explorations had a significant impact on France and King Francis I by giving the king a claim to land in North America for the first time. Verrazzano's voyages in the 1520s helped establish France's presence in the New World, which later encouraged further exploration and colonization efforts. Although he did not bring back vast riches or settle in New York himself, his findings laid the groundwork for future French exploration and claims in North America. So, the most accurate statement would be:
Verrazzano’s explorations gave King Francis I claim to land in North America for the first time.