You're right to notice that Nazi ideology was a bit inconsistent on how to view ancient Germanic history; that's because the Nazi high command couldn't agree on it. For instance, Heinrich Himmler, who was rather anti-clerical and was into esoteric mysticism, despised Charlemagne for his massacre of the Saxons, while Hitler viewed it possibly. Albert Speer's memoirs quoted him as saying: "Killing all those Saxons was not a historical crime, as Himmler thinks. Charlemagne did a good thing in subjugating Widukind and killing the Saxons out of hand. He thereby made possible the empire of the Franks and the entry of Western culture into what is now Germany."

But to specifically answer your question, we can turn to one of the major ideologues of the Nazi Party, Alfred Rosenberg. In 1930, he published a book called The Myth of the Twentieth Century, in which he spends a good portion talking about the history of Europe. In short, it can all be summed up as "good & strong = done by Aryans, bad & weak = done by non-Aryans/Jewish trickery/etc." He took the classical idea of east vs. west conflict and reframed it in terms of Semites vs. Aryans, where strong Nordic empires collapsed because they either intermarried or were intellectually influenced by Levantines (read: proto-Jews). I'll publish some excerpts on how he viewed Rome and its downfall:

The history of Rome essentially parallels that of Hellas, although it is set against a greater expanse of territory and a larger political power structure. Rome, too, was established by a Nordic folkish wave which poured into the fertile valleys to the south of the Alps long before the Gauls and the Teutons. It broke the dominion of the Etruscans, that mysterious and alien near eastern people. (75)

Ancient Rome, about which history tells us little, became a true folkish state through sound breeding, and was united in the struggle against the whole of orientalism. All the brains and strengths, which would be squandered later when Rome engaged in world conflicts, were formed and banked, as it were, in this prehistoric period. (76)

By the middle of the fifth century B.C., the first step toward chaos had been taken. Mixed marriages between patricians and plebeians were made legal. Racial mixing thus became for Rome, as it had for Persia and Hellas, the seed of ultimate decay of folk and state. (76-77)

Influenced by his Syrian mother (daughter of a priest of Baal in Asia Minor), Caracalla, the most loathsome bastard to ever sit on the throne of the Caesars, declared that all free inhabitants of the Roman Empire were citizens of Rome.

So perished the Roman world. (77)

Like a mighty and awesome primordial destiny, the Cimbri had once stormed in from the north. An initial impulse could not stay the Nordic Celts and Teutons from repeatedly pressing upon the frontiers of Rome. In campaign after campaign the military skills of the Romans proved ineffectual against the rude strength of a young people. Giant blond slaves began to appear on the streets of Rome, and the Germanic ideal of beauty became fashionable among a decadent people bereft of all ideas of their own. Free Teutons were also soon no rarity in Rome. More and more the Caesars came to depend for support on the loyalty of the Germanic soldiery. Yet at the same time the Germans came to constitute the greatest threat to the existence of the wretched state now without values of its own. (90-91)

By the time of Constantinus, the Roman army was almost entirely Germanic. Whoever cannot see racial forces at work here must be blind to all historical processes. It is patently obvious that both decomposition and rebirth are present in this. The regenerative process continues past Constantinus to Stilicho, Alaric, Ricimer, Odoacer, Theodoric, the Langobards and to the Normans. These last named started by establishing a kingdom in the south which reached its apogee under the incomparable Friedrich II, whose Sicilian kingdom became the first secular world state, and whose provinces were settled by German nobility.

In this process of Nordicising Italy, the work of Theodoric the Great was particularly significant. For more than thirty years this strong, yet generous and gentle ruler, governed Italy . . . Although unfortunately widely dispersed, nevertheless more than 200,000 Germanic families settled in Tuscany and around Ravenna and Venice. Once again Nordic hands drove the plow through the soil of middle Italy and made the hitherto impoverished and desolate land fruitful and independent of the grain imports from North Africa.

Set apart from the indigenous population by their adherence to the Arian denomination and by laws prohibiting intermarraige, the Goths and the later Langobards played the same character forming role as had the first Nordic immigrants for old Republican Rome. Racial amalgamation only began with the conversion of the Germanic Christians from the Arian creed to Roman Catholicism.

At last came the Renaissance as a thunderous reassertion of Nordic Germanic blood. With a sudden shattering of constricting social barriers, there arose from the cultivated soil one genius after another. Meanwhile, all of Africanised Italy south of Rome remained mute and uncreative, until today, when Fascism, again arising from the north, is attempting to reawaken old values. Attempting! (90-91)

Needless to say, this is all historical bunk. He takes a simplified historical narrative and uses the gaps to project his own racial beliefs on it, and some of his ostensibly historical claims have long since been disproven. For instance, there is no historical, genealogical, or archaeological evidence to suggest that the earliest Romans were migrants from outside of the Italian peninsula, let alone from a Nordic heartland north of the Alps.

If you want to read the full text and subject yourself to lots of dense rambling on how St. Paul ruined all of Christianity, you may do so here. As for the info in the first few paragraphs, I got that from The Holy Reich: Nazi Conceptions of Christianity, 1919-1945 by Richard Stiegmann-Gall.