Well, your question is a little broad. "Europeans" covers a large amount of people, and the discoveries made during that period were received differently by different people. You can look at the reaction of the nobles and merchants financing the expeditions, or the reaction of scholars, or the reaction of the common person. All the reactions will be different, and some we have more information about than others.

The context is really important. Most westward exploration was part of a pretty tentative search by a few major powers for a new passageway to India and South-East Asia. Portugal was monopolizing the eastern route around Africa, which put some pressure on Spain that resulted in them hiring Columbus. When Columbus made his voyages, he was pretty certain that he had found some islands near Japan, and he eventually died still convinced that he had found Asia. But as Spain continued exploring and setting up colonies, they began to suspect that Columbus was wrong. Further exploration by Spain, Portugal, and England confirmed those suspicions. So at least for the Spanish crown, the initial reaction was gradual disillusionment and disappointment, since they had just hit a giant roadblock in their plan to create a competing Asian trade route.

A lot of subsequent exploration was either meant to either find a way around the new land, or to set up new colonies and claim territory. Spain and Portugal had convinced the Papacy to grant them each land on either side of an imaginary line, and were pretty happy to find potentially exploitable land and heathens, even if it wasn't their original goal. They found precious metals and other economic incentives to develop their presence there. For a lot of merchants and nobles, it began to be seen primarily as a new economic opportunity.

As for how it was regarded by scholars--they had a varied, slightly delayed response. The Renaissance was in full swing, and you had a lot of new methods of thought and expression appearing. Scholars mainly focused on classic literature and thought, and the prevailing intellectual attitude was very backward-looking. This persisted through the discovery of the new world, but some historians like J.H. Parry think that the discoveries made contributed to a shift in thought and study that occurred around the same time.

After exploration really started to get underway, you started to see an ever-increasing use for technology in navigation. Astronomy started to get more developed, and some scholars started thinking more empirically (forming the foundations for scientific thought). The process was very slow, and you could always see the influence of ancient works even in pretty radical new ideas like Copernicus' model of the solar system. Aside from new ideas, new technologies started being developed, applying primitive scientific thinking for practical purposes. There was a race to find new methods of figuring longitude at sea, which led to further developments in clocks and astronomy. Overall, the new discoveries and the infrastructure needed to maintain exploration led to what could be characterized as the first recognizable relationship between science and technology.

Not a lot of this was on the minds of the participants. The new world was a pretty exciting prospect, travel accounts(both fake and real) were widely read and distributed, but we're not really sure how the common person reacted, as far as I am aware. But as far as "rethinking everything they knew," you're almost on point. It was by no means immediate, and people didn't abandon ancient thinking for quite some time, but the process of having old conceptions about the Earth proven wrong certainly contributed at least in some way to the rise of the Scientific Revolution.

The discoveries sparked some debate between theologians and philosophers, concerning politics, ethics, and geography. These mainly revolved around the rights of native populations, property rights, and the limits of Papal authority on Earth. The old notions of broad Papal authority over all of Christendom started to seem dubious or at least impractical, given the new known extent of Earth's geography. Before the discoveries, most maps were based on religious conceptions of Christendom and word-of-mouth accounts from overland traders. The Mediterranean was very much the center of the known world up until then, hence its name. As a result, the most visible, direct effects of exploration were on maps and geography. Looking at the maps that developed over that period, its effect was pretty radical.

In the end, the discovery was a big event; it's significance was recognized, but in different ways by different people. It's influence on European thought and society was mostly indirect and gradual, but very notable in retrospect.

Main resources:

J.H. Parry, The Age of Reconnaissance (mainly Introduction, Ch. 9, Ch. 10, Ch 19)

Daniel J. Boorstin's The Discoverers also provides a good popular account of early exploration, its context, and its influence on science and technology.