Much more can be said, but maybe this previous answer can help you.

Overall, they seem to have merged fairly quickly in the centuries after the Fall of Rome, Roman families intermarrying with the new Barbarian nobility, the former adopting the social codes of the latter (up to, eventually, considering themselves as Barbarians with few regional exceptions), the latter largely inheriting the late Roman culture and institutions.

This led to sort of a "Barbarized" nobility as illustrated by early medieval graves : people being buried with Barbarian-looking jewelry made in Constantinople, equipped with Roman weaponry, buried next to their horses but next to a chapel, having runes on their swords or caskets but with Christian scenes or even Latin inscriptions : without further indication, it's next to impossible to say if they were Barbarians chiefs whom lineage could be tied to former federates that were essentially Romanized, or if they were local Roman aristocrats that adopted the social codes of romanized Barbarians.

By the time what we call feudal relations begin to appear (privatization of public power and its merging with land ownership, founded on exchanges of services and honours) meaning roughly the VIIIth to XIth centuries, several families were reputed or claimed descend from Antiquity.

While it's probable that many aristocratic families in the mainland had a general Roman ascendancy, would it be trough the sheer petty number of Barbarians in the Vth century (and a great part of them being "Barbarians of Roman origin" so to say), it's difficult at best to assert the validity of specific claims due to the reconstructed aspect of several genealogies (especially in the case of the late Carolingian and post-Carolingian nobility) and no descent from Antiquity is more than speculated. Carolingians themselves were claimed descending trough Ansegiel from the Syagrii meta-family but this is largely disputed, although it's possible he descended from an unnamed senatorial family by his mother.