Many of those linguistic changes started before or while the Frankish tribal confederacy was formed. The Franks, Saxons etc. developed out of smaller Germanic tribes.
(It's going to be a bit long, sorry, but I think giving the geopolitical context would help to look at linguistical matters. Just skip it if you want)
At the difference of Saxons, that maintained a huge transrhenan presence in spite of migrations, Frankish presence past Rhine is a matter of conquest on other peoples : Thuringians, Alemans, Bavarians, Saxons, Frisians, Bavarians.
All of the Frankish kingdoms in the Vth century (the political unity of Franks then is gone, in spite of obvious unifying factors that Clovis used) centered in Roman towns : Cambrai, Koln, Tournai? (We have limited knowledge on Chilperic kingdom, outside it was centered on Belgica Secunda), Trier (if we consider Arbogast county), Tongeren/Tongres.
Eventually, even with the structural division of the kingdom, the Seine/Meuse region remained the political and cultural center of the
regnum.
That's an important factor there, it means than Frankish Germany wasn't an heartland for Franks, but an extension of their original political center on different peoples, with their own tribal and political identities.
We know, from different sources, that Frankish Germany entities, at the contrary to what existed in Gaul (with the notable exception of Gascony after the VIIth century), enjoyed diverse degrees of autonomy. Duchy of Thuringia, Alemania, Bavaria; and that the maintain of "national" (you'll pardon me the anachronism) laws was almost systematical and be pursued with Saxons, during Charlemagne's reign, in spite of an harsh conquest.
Austrasia itself, often looked more on Gaul than Germany, with part of Gaul (as Provence or Aquitaine)
falling under its juridiction.
It's not before the end of Dagobert I's reign, that Austrasia would definitly be distinct politically. And that interestingly in the same time Peppinids raise in power.
Peppinids were a family with huge ties on the eastern part of the regnum, and close to the Church, trough Arnulfings at first, then trough a really consistant policy (that implied a missionnary policy on Germany, therefore a Frankish presence trough Christianism)
Their interests being present mostly on Rhineland, more they took dominance over Austrasia and then on all Frankish kingdoms. Frankish presence, and not only domination, as Fulda or Frankfurt creation aren't really something before the late VIIth century.
Eventually, the political center shifted from Seine/Meuse to Meuse/Rhine, fitting Carolingian hegemony.
When Carolingia will fall in the IXth century, the division of the empire was made along these lines, with language having a
symbolical charge. Each king had his own, in spite of being all Franks, using it for its troops.
Of course, we're talking about speeches that aren't yet that defined : gallo-romance from one (maybe with more or less artificialities to be understood by everyone), early althochdeutsch (and not Old Dutch, or language more closely related to what we know of Frankish).
At this point, and while it can't be only explained trough this, and knowing that this period is a period of linguistical differenciation in the region (both from romance languages, partially due to the carolingian policy to renovate classical latin; and germanic speeches as well) one can wonder if the linguistical germanisation of Rhineland isn't due less to a Frankish presence there, than to political and cultural events.