The status of Jews in Gaul during the Merovingian era was ambiguous, although certainly more precarious than those of Christians, especially as society and its institutions became inherently Christian by the mid-VIth century : their religion was licit but considered as a lasting counterexample for the broader community and ideally set apart from it, although it seems that they were at least partly culturally integrated into the broad horizon of early medieval Gaul while the recurrence of antijudaic prescriptions in Merovingian synods point both this institutional hostility and its relative difficulty applying them.

Jews were freemen, able to own property, to farm lands or any partaking in any activity of their time, having a legal existence, but whose freedoms would be limited according the Theodosian Code, that is being put in a systematic inferiority, eventually dependent from local or royal authority in its (rare) benevolence or (more commonly) hostility, being legally forbidden to hold official charges (and by the VIth, effectively to hold any kind of delegated power) over Christians : occasional forcible conversions or expulsions (in imitation of Eastern Roman decisions) were generally frowned upon by the Latin Church but abuses were rarely punished.

Due to the lack of mention in Frankish sources, and the utter lack of preservation of Gallic Jewish sources, we're not informed about their situation during the Merovingian decline and Carolingian takeover : we can still point that the Frankish conquest of Gothia (the part of Gaul still held by Goths until the VIIIth century) put early Carolingians in contact with its dynamic Jewish communities (especially in Narbonne) : while it's plausible that Jewish communities were present in the homelands of the "pre-Carolingians" in Austrasia, and thus already in contact with the rising dynasty, it remains largely speculative and probably of secondary importance.

Still, there were Jewish communities present in the main cities of Gaul, especially in the South (as they find a refuge when expelled from northern cities into probably stronger communities), where were found craftsmen and traders in nobiliary clientele and service.

Already coping with slowdown after the fall of the western Roman Empire, Mediterranean trade already was noticeably declining by the mid-to-late VIth century (for reasons hard to pinpoint, but probably including the Roman-Persian wars and a lower influx of gold from Constantinople, the Justinian plague, a growing unpopularity of the Eastern Roman Empire, etc.) with the disappearance of 'Syrian' (that is Greek or Hellenized Easterners) traders in Gaul and by the early VIIIth a virtual cession of regular trade between Constantinople and Italy. Jewish communities in southern Gaul remained the best access point to eastern products and would be particularly noticeable in this "international" function along the Carolingian period, and often called in contemporary historiography 'Radanites' (a name of unclear origin, either in reference to the river Rhône or a location in Mesopotamia/Persia) even if the term rarely appears and only later on in the description made by Ibn Khurdadhbih

These traders speak Arab, Persian, Greek, Frankish [that is the languages spoken in Francia], Spanish and Slavic. They travel from West to East and East to West partly on land, partly on sea bringing from there eunuchs, enslaved women, young men, silks, castors, martens and other furs, and swords. [...]

[From China] they carry musk, aloes, camphor, cinnamon and other goods from the eastern lands. [...] Some are going to Constantinople to sell them to Romans; other go to the palace of the king of Franks to sell their goods there.

It is followed by a description of their trade ways, and while the description was written ca. 840, it can be considered as a fair speculation what it looked like in the heydays of the Carolingian Empire that is as an extension of a largely Arabo-Islamic ensemble.
It shouldn't be conflated with the notion that merchants were essentially Jewish however, as Frankish, Frisians or Scandinavian traders in North Sea (where Jews seem to have been absent) or Christians (probably mostly Italians) along Jews in the Mediterranean Sea. But as a set of related communities (as 'Syrians' or 'Frisians'), and an easily identified one in Latin Europe, they were both more noticeable and cohesive.

Charlemagne is recorded twice having resorted to Jews as royal agents, something that did not happened since the mid-to-late VIth century in Francia, for his own procurement of precious goods (De Carolo Magno, I-17) but also in diplomatic exchange with the Abassids (Vita Karoli), and its probable that at least part of the Judaic policies of his successors were inspired or taken from his own, such as the novation of a 'Master of the Jews' that is an official appointed as an intermediary between the palace and a Jewish community.

(A.J. Zuckerman famously argued that Peppin had created the nucleus of the Jewish princely community of Narbonne by appointing a Davidic descendent as count, but this is largely ill-considered and we don't know what was the attitude of the Jewish communities in the region towards Franks, although potentially one of cautious neutrality : the much later XIIth century 'Epic of Charles the Great in Carcassonne and Narbonne' or 'Pseudo-Philomena' credit the Jews of Narbonne surrendering the city to (sic.) Charles but it's a mix of annalist history, regional tradition and straight-up fiction and thus hard to interpret besides the parallel with medieval Jewish tradition of a prestigious and institutional presence of Jews in Narbonne.)

It is significant that part of the recorded exports from Francia were slaves, likely less obtained from raids after the VIIIth century (although the general disorder coming from Carolingian collapse did certainly led to this again) than taking/buying them from clients (e.g. Moravians, Odrobites, etc.) or neighbours beyond their realm : how much the trade was important is debated (from being marginal to having fuelled the Carolingian-era trade boom) but along with furs were products obtained from territorial hegemony and connection to markets and trade roads connected to the Mediterranean and Near-Eastern ensemble (from Francia or Italy to Spain, Sicily, Maghreb, Africa, Constantinople and Caspian Sea) and obtaining in kind monetary from sells, but also tolls (interestingly Carolingian silver monetary value is similar to those of Umayyad Spain) and critically eastern Mediterranean and Asian products. It's not clear how much part Jewish traders took in transmaritime slave trade, certainly not exclusive, but specialized enough in Arab sources.

Jewish life in Francia shouldn't be restricted to being trade intermediaries : we know they farmed land (communities in Gaul being known to produce and sell wine, including for the Eucharist), were involved in leather and textile production (including Christian religious clothing), had a cultural life (partly born out of tighter regional connections), partook in productive activities with Christians (they could employ or be employed by), etc. But this seem to be largely why Carolingian kings, and Frankish aristocracy, searched a mutually beneficial association. It is otherwise possible that the alliance between Carolingians and the Papacy made the former more inclined to respect the official stance of Rome on this regard, that is of legal protection and punishment of abuses albeit less for the sake of religious tolerance than being counter-productive when it came to conversion, mortal danger of apostasy and general fear of 'judaizing' Christians.

Louis the Pious and his successors during the IXth century would continue, or even expand, on this policy and that's where we have most of our understanding of the relation between Jews and Carolingians : besides the appointment of specific officials, Jewish traders could obtain special privileges such as seeing their fair or harbour tolls being waived, being able to rebuild their synagogues, to benefit from partial self-rule under Imperial patronage, being called under royal or imperial authority to settle or join an existing community in Francia as Charles the Fat did with Luccan traders called to inhabit Metz (it is noteworthy that the main Jewish families in high medieval Languedoc born Greek names). Basically holding a legal/para-legal status equivalent to Jews as dhimmi in the Arabo-Islamic world, but making them all the more dependent of royal protection, and with an explicit legal inferiority (paying heavier taxes, requiring more witnesses than Christians in legal matter, being subject to specific judicial ordeals they were spared so far, etc.).

Eventually, the core principle that they couldn't at any point be in a position of power over Christians stood both in realities and ideas.