I know that the Norse people didn't convert until the 900ish. But I'm wondering how come tribes like the Franks and Gothics converted so easily.
By the 4th century CE, the conversion of the Roman Empire had already led to the close identification between the identities of romanitas (Roman-ness; civilisation) and Christianity [http://tgenloe.com/sc/?p=662]. This was an idea that was quite popular (and one, incidentally, that was rejected by Augustine of Hippo).
Within that context, conversion to Christianity was closely related to depth of interaction with the Roman Empire, and, secondarily, the desire to be considered 'civilised'. From Peter Heather's Empires and Barbarians:
As the literate religion of the developed imperial world, backed by all the ideological cachet that perceived success imparts by association, Christianity usually 'won' in the culture clashes of the early Middle Ages: in much the same way, I suspect, that Levi's and McDonald's have been adopted the world over because of their association with the winning world brand that is America. Just occasionally, though, exposure to Christianity generated a violent and opposite backlash... [e.g.] when the leadership of the fourth-century Gothic Tervingi started to persecute Christians because they associated the religion with Roman hegemony.
It's therefore unsurprising that the Franks and Goths converted relatively early - they were neighbours to Rome's Mediterranean-centred civilisation. They were therefore closely connected to the Roman world through trade and war (as enemies, mercenaries, and foederati) and even language (Latin). Therefore, they were arguably most exposed to the influence of Christianity, most accessible to Roman missionaries (whether Catholic or Arian), and most aware of the potential benefits and prestige of Roman civilisation.
In contrast, the Norse existed on the fringes of the Roman world and hardly featured in Christian sources until the raids on the British Isles in the 9th century. Hence, much less interaction with Roman/Christian civilisation, fewer opportunities for missionary work, fewer incentives to take up Christianity. But once the interactions started taking place, the same factors I outlined in paragraph 2 started to operate - and the Norse picked up Christianity relatively quickly. Same applies for the barbarian tribes on the outer fringes of the Roman world - whether they were Germanic-speaking (e.g. the Saxons), Norse (and Rus), and Slavs.