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Say Eric The red's expedition is incredably sucessfull, and not only does a persistant colony in Greenland get started, but The Norse Culture Spreads down to US coastline, interbreeding and Flurishing in The Americas, forming a Althing type Democracy.

300 Years later, Columbus finds Viking trading posts in the Carribean, What is Isabela's Response

How does this extensive trade network up and down the Atlantic coast of North America effect the Hundred Years Wars?

Do The Puritan's attempt to cross the Atlantic and Settle in the Norse controlled Lands?

First, it would have required a much denser population. This could have drained a large number of folks from Europe, and caused the Norse to be much less active in Europe. Potentially, this could have caused drastic changes in history. One of the biggest potential changes would be in the history of England. With adventurers being drained off to settle N. America, Harold Hardrada might have not have had enough warriors to press his claim to the English throne in 1066. Without that distraction, Harold Godwinson might have been able to defeat William of Normandy. There has already been a ton of alternate histories done based on a Saxon victory in 1066. To address at least one of your questions, without the Norman Conquest, there would have been no Hundred Years War at all.

Even if the Norman Conquest happened as scheduled, the consequence of extended contact with the Americas would be great for Europe. The Norse were not isolated from the rest of the Continent. If they had maintained a constant contact with America, which would be required for a sizable Norse population to flourish here, then the knowledge of its existence would have trickled down throughout Europe. Europe would have been introduced to the potato and maize much earlier. The "Age of Exploration" would have panned out quite differently. It is doubtful Columbus would have made his voyage. If there was sufficient trade along the Nordic Route, the Italians and Portuguese and maybe the Spanish might well have sought a more direct route to the New World.

If however the Nordic trade was not very profitable, as would be likely, then there might have been not other European conquests in the Americas. Certainly, the English and French would not have been able to colonize. Possibly the Mediterranean states might have tried to colonize, but they might have found the civilizations to be more robust. The native populations would probably have already been exposed to European diseases, and they might have obtained various domestic beasts from the Norse, including the horse. They would have gained at least some knowledge of iron and steel. The Mediterranean explorers could have met horse riding peoples with swords and metal tipped spears and long bows.