The Germans were known as devout Arians since at least 2nd century. Some Roman generals were known as Arians in the 4th century. But somehow in 9th century we already have Charlemagne's rule blessed by Pope Leo III, the Nicene orthodoxy.
How did Arianism disappear from European religious landscape?
Wikipedia's page on Arianism doesn't seem to be that useful; it only has this short passage,
By the beginning of the 8th century, these kingdoms had either been conquered by Nicene neighbors (Ostrogoths, Vandals, Burgundians) or their rulers had accepted Nicene Christianity (Visigoths, Lombards).
What was the process that lead to the eventual disappearance of Arianism? Why did the Ostrogoths, Vandals, Burgundians, Visigoths, Lombards not find Arianism that appealing?
First, your information is misguided. There aren't any Arians in the 2nd century, let alone German ones. Arius doesn't appear on the scene until the early 4th century, and is roundly condemned at Nicaea 325.
Now, I'm just going to indulge in some copy/paste from an earlier answer that I did:
Arius, a presbyter from Alexandria, acted as a catalyst for theological controversy in the early 4th century, by going head to head with his bishop, Alexander, on key points of doctrine about how to understand the relationship, and the metaphysics, of God as Father and the Christ as Son. Basically Arius held a position in which the Son was a separate entity, created at a certain point in time, and not recognisably ‘god’ in the sense that later Christians would hold. It’s much more complicated, but that’s the gist. This was pretty much boiling over just after Constantine I came to power, and Constantine took as part of his job keeping the church unified, hence you end up with the first ecumenical council, Nicaea, in 325, which pretty much done and dusted Arius and his ideas. However, it also revealed that there was far less consensus about some of these issues than perhaps, naively, the bishops had earlier believed. Essentially a large portion of the next 60 years was spent in vigorous theological debate about what exactly that Father-Son relationship was and how it functioned. We now generally avoid the label ‘Arianism’ for one side of that debate, for two reasons: there was more than ‘one side’, and it’s not very accurate. However, there were factions that showed more similarity with Arius, and they have traditionally been called ‘Arian’, ‘Arianist’, etc., largely because Athanasius who turned out to be on the winning side made it a habit of calling his opponents that. It’s during this period that you see more and more encroachment for the ‘Barbarian’ tribes, Goths et alii, who are pushing on the Empire’s porous borders. The most famous Goth, at least for our purposes, was Ulfilas, who ended up being ordained as a bishop by Eusebius of Nicomedia. Ulfilas is also responsible for the Gothic translation of the Bible, and almost all we have left in terms of Gothic texts is biblical texts. Anyway, what faction was Eusebius of Nicomedia on in those theological debates? You guessed it, the later-declared-non-orthodox side that generally is called ‘Arian’. So what ‘version’ did Ulfilas take to the Goths? Arianism. This is all happening in the mid 4th century, while those theological debates are going on, and they’re almost entirely happening in Greek (a little bit in Latin). So once ‘Arian’ Christianity starts spreading among the Goths and other barbaroi, they essentially maintain a kind of autonomy. When things finally get settled around 379-381 and the Council of Constantinople, that is a theological-political solution that doesn’t really get brought to bear on the barbarians, who essentially function outside the structures of the Empire and the Graeco-Roman Church. Hence, they continue on as ‘Arians’. But it’s difficult to trace what kind of Arianism they had because we have little documentation of this kind. As I said, most of the Gothic we have is simply biblical texts. It’s even worse for the other types of tribes you have in mind. The Visigoths who ended up in Spain eventually embraced Nicene Christianity at the 3rd Council of Toledo in 589.
So, I know that doesn't answer your question, but it does fill in some gaps. Now, how did Arianism disappear?
In Spain it disappeared thanks to rapproachment with Catholics, hence Toledo in 589. In North Africa it survived most until the Arab Conquests swept westward. In France... well you need to understand that 'Romanisation' was particularly successful in what's now Italy and France, and that although incoming barbarian tribes did 'take over', they generally did so by becoming a social elite which often adopted Roman(esque) social patterns and order. They deliberately imitated Roman culture and ideals, and they were not overly disruptive to the existing church structures in those regions. That meant that while the ruling elite might be Arian, the dominant church was Nicene through and through. Arianism's death in this context has probably more to do with the social interactions of a 'foreign' elite and the local cultural majority, than with any philosophical or theological waning of Arian thought in those contexts.