This is a pretty broad question, and it has a lot of different answers. In the pre-Christian era, before the Saxons were subdued by Charlemagne (the Saxons lived directly south of Denmark), they shared some religious traditions with the Danes that we normally think of as Norse. For example, the idea of a tree that holds up the world (Yggdrasil) had its parallel among the Saxons (Irminsul, a tree or pillar), where sacrifices would be made and caches of gold and silver would be buried.

Other forms of influence was more direct. For instance, it's recorded in the Royal Frankish Annals that a Danish king named Godofrid (Godfred), in 808, wrecked a trading town called Reric in northern Germany and resettled its merchants in Danish territory, possibly at the now-excavated town of Hedeby. It's further recounted that this king warred with the Obodrites, a people to the south-east of Denmark.

As I mentioned, Charlemagne eventually (after a great deal of bloodshed) conquered the Saxons, converted them to Christianity and incorporated them into the Carolingian Empire. We know from the Annals, and their successors, the Annals of St. Bertin, that there were no open hostilities between the Danish state and the Frankish empire after 814, when Godofrid died--the presence of the Danevirke, a huge, wood-fronted earthen wall, cutting off the neck of the Jutland peninsula, probably had something to do with this. However, there was plenty of intrigue going on! The Franks made several attempts to back a claimant to the Danish throne called Harald, with varying degrees of success, and Danish pirates frequently sailed down the coast to Frisia and plundered or burned its trading towns. It seems to have been common for exiled Danish claimants to the throne, such as Harald himself in his later years, to retreat down the coast and make a living plundering Frankish settlements, perhaps hoping to accumulate enough wealth to make possible a return to power in their home country.

This is all a little far afield from the question of culture, but it should give you an idea of what kinds of relations the Danes (which were probably the majority of the Viking raiders on the Continent) had with their southern neighbors. I specialize in the effects of Viking raids on present-day France and the Low Countries, so I don't have much information about Northern Germany. However, I can give you a little information about the politics in the region, and why everything eventually went to hell.

Basically, after Charlemagne died, his son Louis the Pious ruled an enormous empire; most of modern France and Germany and Italy was under him or ruled by his sons, who acted as sub-kings. However, there were two major rebellions against him, instigated by his son Lothar, sub-king of Italy. During the periods of general war, the Vikings, sensing the opportunities presented by a lack of order, would swoop in and raid monasteries and trading towns on the Frankish coastline and up the Seine and the Loire river valleys. This happened again during the war after Louis's death, between his sons, from 840-3. The realm was split up between them, and Louis's son Louis the German got the East Frankish area, some of which we now call Germany (with considerable fudging around the borders). Charles the Bald, another son, got West Frankia, across the Scheldt river from Louis.

I don't know what-all happened in East Frankia between 843 and 876, when Louis the German died. The Annals of Fulda record that time period in East Frankia, but I couldn't find a free online English version, so I would advise you to look that up or ask someone who has a copy to do so. After that, the kingdom was absorbed back into the Carolingian Empire under Charles the Bald. Charles died in 877 and basically anarchy descended on Germany. There's accounts of wholesale plunder and pillaging of German cities, even of Aachen, the former imperial capital, by armies of Vikings. The Annals of St. Bertin tell us this:

"The magnates of the kingdom sent a swift messenger to Carloman asking him to leave the troops who were besieging Vienne and trying to put down Boso's revolt. The magnates said he should make haste to come to them as fast as he could, since they had made all their military preparations for a campaign against the Northmen who had burned the cities of Cologne and Trier and their adjacent monasteries and had got control of the monasteries of St-Lambert at Liège, Priim and Inden and even the palace at Aachen and all the monasteries of the neighbouring dioceses, that is, of Tongres, Arras and Cambrai and part of the diocese of Rheims, much of which they had burned, including the fortress of Mouzon."

After Charles died, the Frankish kings became much weaker. Charles the Fat was a fairly ineffective ruler, preferring to pay off the Vikings instead of facing them in battle. For at least the 880s, the Vikings tended to do as they pleased most of the time, famously laying siege to Paris in addition to the incursions described above. After that is when my experience mostly ends, so I hope a 10th-century expert comes in after me.

To summarize: The Danish kings made armed incursions to the south when it was just the Saxons and Obodrites, but seem to have stopped open war once Charlemagne moved into the area and conquered the Saxons (and Louis the Pious and his son Louis the German). However, there was frequent low-level pirate warfare between roaming bands of Danes (and Norwegians, and maybe some Swedes) and Franks. We know that the pre-Frankish Saxons and Obodrites shared at least some religious characteristics, and given the existence of Reric and later Hedeby, we know that a lot of trade went back and forth between the Danes and their southern neighbors. (Actually, the Danish kings made a lot of their money through taxes on merchants.)

Beyond that, however, I can't tell you a lot about whether the Vikings changed the culture there. Unlike in England and Iceland, there wasn't much settlement by Vikings on the Continent, with the exception of Normandy and a few pieces of land (like the former island of Walcheren) that were given to Vikings for a time, but that seems not to have lasted. We know goods passed between them, but I at least do not have anything more helpful for you.