I'm going to do my best in answering this question as I feel it falls in my wheel house and I'm actually reading two books on the Gothic and Frankish peoples.

Starting off with the first part of your question I just want to make a minor correction.

The Franks became Christian much earlier than many other Germanic groups. Why is this?

The Franks actually didn't become Christian earlier than many other germanic groups, for example Orosius of the 4th century writes.

The barbarians, detesting their swords, turned to their ploughs and now cherish the Romans as comrades and friends, so that now there may be found among them certain Romans who prefer poverty with freedom among the barbarians than paying tribute with anxiety among the Romans . . . throughout the East and the West the churches of Christ were replete with Huns, Suevi, Vandals, and Burgundians.

This is nearly 100 years before the conversion of the Franks, and there were already Vandal, Burgundian and Suebi Arians. So the Franks weren't the first to convert, but they were the first to convert to Orthodox Christianity, and the Frankish tales of Clovis' conversion are very romantic and remembered well. The story of Clovis and his hour of agonising prayer on the field of Tolbiac, and, perhaps most of all, the love and persistence of Clotilda, his wife, during their infants sickness is still taught in churches today.

So why did the Franks convert?

That's a harder question to answer. The preferred and best way of converting a population to Christianity during this time was to convert the local nobles and ruling lords, then the religion would shuffle down through the masses as laws and positions of power favoured those who followed the ruler's religion. So what the average person gained from converting was a lot more personal, things like having a greater connection with their community, a more secure afterlife, organized temples and churches that were all around Europe and obviously any personal or cultural influences that they might encounter in their daily lives.

As for the leaders it's a bit easier to see why they would convert, it allowed them a cultural tie with the Roman Empire that still stood in the East and the Papacy that remained in the West. Every local warlord wanted to be seen as the successor to Rome, and many had claimed that title during the Imperial Crisis of the 3rd century and the following centuries. Christianity granted Germanic kings who converted a powerful ally in the Church and legitimized their rule in the eyes of their non-pagan followers, but they also used it as a just cause to invade neighbouring pagans and heretics, such as when Clovis invaded Aquitaine under the pretense of liberating oppressed Catholics under Arian rule. Of course converting to Christianity would also help unify the realm and keep qualms from religious differences to a minimum, but it certainly helped the conquered Christian people feel reassured their lord wasn't a savage pagan. But of course a ruler like any other person would have personal reasons too, maybe one of their children died with pagan prayers but their next lived after being baptised, or maybe they married a Christian wife.

I can't really speak to when the last hold out of Germanic paganism was or where it was in Francia so hopefully someone else can answer it, but if you have any followup questions I'll do my best to answer them.

Sources

The Franks by Lewis Sergeant

The Story of the Goths by Henry Bradley

Historiae Adversus Paganos by Paulus Orosius