I'm not sure I entirely understand your question. Earlier I wrote an answer to a question asking about conflict between Christians and Pagans in the 9th century, that may shed a little light for you.

Otherwise it's hard to give a general answer - and "pagan" can mean many things, to a Christian at certain times it could even mean Muslim. If you're talking about how state heads approached one another then that would be more down to politics and alliances than religion, although naturally religion would have already coloured those things in the first instance.

What do you mean when you say they were "of the same heritage"?

I might have misinterpreted your question, but what I think you’re asking about is how people who had converted to Christianity view their pagan ancestors or folk heroes. Often, we see that pagan folklore or legends were Christianised after a particular tribe or group of people were converted. One reason why this happened so much is because in much of northern and western Europe after the fall of the Western Roman Empire, Christianity and literacy went hand in hand. Nearly all our surviving texts were written after these people were converted to Christianity, and so by the time folklore or mythical origin stories for a particular race of people were written down, they had already been transmitted orally through a number of generations of Christians. Let’s look at a few examples of clearly pagan stories that have been Christianised or incorporated into Christian narratives. The first is from a book called The History of the Lombards, written by a Benedictine monk called Paul in the late 8th century, which tells the story of the Lombards from their mythical origins in Scandinavia right through to near-contemporary events, ending with the death of King Liutprand in 743. Paul describes the early history of the Lombards and why they left their (mythical) point of origin in Scandinavia, and includes the following short story about how the Lombards got their name (Lombards was originally Langobards, which means long-beards):

At this point, the men of old tell a silly story that the Wandals [the Vandals, a Germanic tribe] coming to Godan besought him for victory over the Winnili [a different tribe] and that he answered that he would give the victory to those whom he saw first at sunrise ; that then Gambara went to Frea wife of Godan and asked for victory for the Llrinnili, and that Frea gave her counsel that the women of the Winnili should take down their hair and arrange it upon the face like a beard, and that in the early morning they should be present with their husbands and in like manner station themselves to be seen by Godan from the quarter in which he had been wont to look through his window toward the east. And so it was done. And when Godan saw them at sunrise he said: "Who are these long-beards?" And then Frea induced him to give the victory to those to whom he had given the name.' And thus Godan gave the victory to the Winnili. These things are worthy of laughter and are to be held of no account. For victory is due, not to the power of men, but it is rather furnished from heaven.

Godan here is Wotan — the Germanic name for Odin — and his wife Frea is, similarly, the pagan goddess Freyja. For ‘the men of old’ that Paul refers to, this would have been the end of the story, but such pagan ideas are not acceptable for Paul. Paul is a Christian, and so he asserts that it ‘a silly story,’ and that ‘these things are worthy of laugher’. How could a man grant victory, when ‘it is rather furnished form heaven?’. We have a pagan legend clearly preserved in a Christian text, but its pagan character is being stripped away.

The next example comes from Asser’s Life of King Alfred, an account of the life of King Alfred the Great, who ruled the kingdom of Wessex from 871–889. By this point, the Anglo-Saxons had been Christians for several centuries, and Christianity was a central part of their identity — and God was especially important for Alfred and Asser because Alfred spent most of his reign fighting against the pagan Vikings. Asser opens his work with an account of Alfred’s birth, and then lists Alfred’s genealogy:

His genealogy is woven in this way: King Alfred was the son of King Æthelwulf, the son of Egbert, the son of Eahlmund … [about 15 names omitted] the son of Brand, the son of Bældæg, the son of Woden . . . [a few more names omitted] the son of Geat (whom the pagans worshipped for a long time as a god).

In pagan times, of course, the kings would have claimed descent from the pagan gods. In the 890s, in Christian Wessex, they were still doing so — but the gods were not actually gods, merely men. What’s more, they were men who were descended from biblical figures:

Geat was the son of Tætwa . . . [more names omitted] the son of Seth, the son of Noah, the son of Lamech, the son of Methuselah, the son of Enoch . . . the son of Cainan, the son of Enos, the son of Seth, the son of Adam.

So there you have it. Pagan legends are Christianised, and rather than being descended from Woden, the Anglo-Saxon kings are actually the descendants of Noah, Cain, and Adam!

If you’d like to read either of these texts for yourself (and I recommend them, they’re good fun), then there is a good, cheap Penguin Classics version of Asser’s Life of King Alfred, translated by Simon Keynes and Michael Lapidge. The History of the Lombards is slightly harder to find, but the first English translation was made in 1907 and so is now freely available on the Internet Archive — just search for the translation by William Foulke.