They didn't convert from Arianism to Nicean Orthodox, they went straight from pagan to Nicean. So the Franks never had to do the same dance with an Nicean Orthodox populace and clergy that the Arian Germanic tribes did.
Also, the Franks did the least moving around. With a settled core of territory around the Rhine valley they were able to support later expansion. Also, notice that their core territories was not heavily Roman- that is, the Franks were not vastly outnumbered by the people over whom they ruled- actually most of the core Frankish territory was east of the Rhine, and outside the Roman Empire.
The Franks were also the first German tribe to win Roman (the Roman Empire with the capital at Constantinople) recognition of their independence. I believe that Justinian recognized their independence when he ordered the invasion of Italy (beginning the Gothic Wars). This meant that when the Franks eventually expanded into former Roman Imperial territory they didn't have to maintain the dual legal systems that the other Germanic tribes employed (one Germanic, one Roman).
So the Franks were able to maintain the monopoly on military service that the other Germanic tribes had already claimed, but they did so while embracing the religion of the populace, and with the legal blessing of the Roman Empire. All this happened while the Vandals were destroyed by the Eastern Romans, the Ostrogoths were caught between the Eastern Romans and the Lombards, and the Visigoths declined and were then destoyed by invading Moors. So the Franks were the last tribe standing, were politically and religiously acceptable, and had the military ability to both protect (Tours, the Spanish March) and expand (Saxony) Roman Christianity.