Say we're in Paris circa 500. Would there have been two distinct communities of Romance Latin-speaking Christians and Germanic Frankish-speaking pagans? Would the Romance Parisians have been "high society" and the Franks "low-society" or the other way around?
How about 800? Is there still an ethno-linguistic distinction between those more "Roman" and those more "Frankish"?
This is a sticky and much debated question!
The difficulty is, it's not entirely clear who the Franks were. The old view, that they were a cohesive group of warriors who immigrated (violently) from Germany, has been thoroughly discredited by the past two decades of academic work (though its ghost continues to haunt some scholarship and popular histories). Who precisely they were instead has been harder to establish, but it seems likely that they were actually a group of people formed out of the collapsing Roman army in the fifth century (cf Guy Halsall, Barbarian Migrations). So instead of thinking about Germanic, Frankish invaders vs. Latin, Roman natives, it's probably more correct to think about members of a military elite who had seized power from the collapsing western empire, and the civilians whom they ruled.
There were important differences between late Roman civilian and military elites. They dressed differently (the Roman army favored 'barbarian' trousers, for example, and military belts as badges of office; see P. Von Rummel, Habitus Barbarus for a lengthy discussion [in German]), and had different educations (the civilian aristocracy was educated in classical 'paideia'; classical education was less common in military circles; cf P. Brown, Power and Persuasion).
There were also a lot of similarities - both the 'Franks' and 'Romans' were orthodox Christians, and there's little evidence to suggest the military rulers weren't as Christian as the rest of the population (cf B. Effros, Body and Soul).
Things varied by region - in the north, educated Latin culture seems to have not been valued, and it disappeared for a while. In southern France, it survived better, and some elites continued to leave Latin inscriptions commemorating their lives for centuries.
Most clearly, several of the law codes distinguished between Roman and Frankish persons. Franks generally had to produce fewer oathkeepers (trustworthy friends) to swear to their innocence, and had to pay lower fines if convicted for certain crimes than their Roman counterparts. But it's not clear (and still debated) what made someone a Roman or a Frank for the purposes of these laws - military participation, language, or birth.
By 800, these legal distinctions disappear, and Charlemagne chooses to rebrand his kingdom as a new Roman (instead of Frankish) empire.
hi! FYI you may also find something of interest in this section of the FAQ (link on sidebar)