How did their language eventually come to lose its Germanic roots and become a Romance language? Why didn't this occur to tribes east of the Rhine?
The Franks were already heavily integrated into the Roman system by the time they took over Gaul. They were less a distinct people group (with, say, ancient cultural traditions that might help them to keep a distinct sense of separate identity) than they were a political-military organization that grew out of the empire's need to farm-out some of the responsibility for guarding the northern frontier to a group that wasn't part of the overextended regular army. The Franks formed a treaty with Rome, and this treaty gave them the political legitimacy they needed to make a strong position for themselves as a distinct group inside the empire and, eventually, to take over full administration of one of its regions.
So many individual Franks must have spoken Germanic languages initially (many of them would have come from families connected with various Germanic peoples, and many - but certianly not all - had ancestors from the northern side of the frontier), but they were already used to working inside Roman administrative structures by the time they assumed full control over those sturctures at the end of the fifth century. Because Roman government, and Roman civilians, spoke Latin, the Franks chose to follow suit, and they wrote their laws in Frankish and mingled, very quickly, into the local population (there remained legal distinctions between 'Franks' and 'Romans' in some of their law codes, but the boundaries between these two categories seem to have been less a matter of fact and more a question of whether you could successfully pass as a member of the new military aristocracy - as many old Roman families quickly learned to do).
So while there are some individual words from Germanic languages that snuck into Latin (and French, I'm sure you know, evolved out of that Latin over the succeeding centuries), the linguistic makeup of Gaul remained relatively unchanged by the new elites.
Hi, there's always room for more discussion, but fyi, you'll find some previous posts on this topic in the FAQ
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