By the end of the Vth century, not much remained of Gaulish culture in Gaul.

Gaulish language was virtually gone: words in Gallo-Romance languages all passed trough Latin, hinting that even if peripheral linguistic isolates might have existed (North-Western and Alpine regions are usually mentioned but also debated), they didn't have a great relevance they were irrelevant. Gaulish language itself is poorly attested past the IIIrd century, with half-Latinized words until the Vth (the mentions of "Gallic language" are likely about Vulgar Latin).

While Breton is unmistakably a Celtic language, it is also unmistakably a Britonic language akin to Cornish and Welsh carried by British migrants in Late Antiquity : there's a disputed theory proposing a Gaulish substrate on Vannatais dialect, arguably.

The quick latinisation of Gaul was, at least in part, heavily political (borrowing from an earlier answer).As soon as the Ist century, when Claudius granting Latin Law to the three provinces of Gaul (Narbonensis already having obtained it), the re-foundation of Gaulish citiesas Latin or Roman cities created an institutional frame for latinization.

Latin was, by the virtue of being written, omnipresent and monumentalized to a point Gaulish never was (while Gaulish language was written, it remained either practical and ostentatory in a largely oral society ); leading to a quick language shift in elites and the new urban centres that became the institutional and cultural strongholds of Roman Gaul : if the old Gaulish institutions survived, they were transformed (such as the All-Gaul Council, a political and diplomatic assembly being transformed into the Assembly of the Three Gauls, mostly religious with a slim political role in being the direct link between Gallic elites and the emperor) or simply disappeared (Gaulish senates, vergobrets, gutuaters, druids, kings, etc.) when they became, from peregrine cities, Latin or Roman after the Ist century AD; not that it was imposed on them, Gallic elites actively requested it from the emperors.

You're right to mention religion as a key feature there, as a good part of what we know or assume about pre-Roman Gaul is depending on it. For a long time, there was the notion of a "Gallo-Roman religion", a mere interpretation of a Gaulish spirituality. But while some gods in Gaul still bear their (romanized) Gaulish names as Epona, or some other are "tribalized" as Mercury of the Arverns, they are systematically represented and worshipped on Roman lines already by the Ist century CE (for instance, in the Pillar of Boatmen of Paris : displaying "Gaulish" gods in roman fashion, on a votive column unknown from Gauls before the conquest).When it come to traits of Gaulish religiosity before the conquest, it's largely gone : open sanctuaries are gone or replaced by roman temples; animals are sacrificed in Roman fashion (although there were limited differences in the usual sacrifices, they were some such as in the sacrifice of dogs), Druids (although more theologians than priests) are shown the way out, Roman gods pops everywhere and local people even take their tribal deities from them (Mars Mullo or Mercury Arvernos being unattested in this form or other before the conquest, etc. (there's a short answer on the three-headed god appearing in the IInd century AD)

What remained of it? Some names, some displays of heavily re-interpreted attributions; which were no more Gaulish in essence than modern Christianism or Islam are culturally Jewish. What kept a distinct Gaulish aspect the most was arguably the cult of springs among the rustici, but there again, we'd be talking of a creolized cult, that while took on a pre-Roman tradition was transformed by the new dominant culture. Eventually, with the Christianization of Gaul, the same springs and devotions would be hijacked by the new religion and re-interpreted without anyone going at Lourdes nowadays undergoing a Gaulish devotion.

What formed the core of Gaulish spirituality, the stress on the cosmic movements and cycles (including, but not only, soul transmigration); a ritual devotion in semi-public sanctuaries were gone even before the Late Antiquity.

Interestingly, cultural (both material and immaterial) romanisation seems to have happened even before the Caesarian conquest : Roman trade carried over trough Celtica (in opposition to Belgica, where Caesar acknowledge a much lesser Roman influence among Gauls) a "Roman way of life" leading several Gauls to adopt some Roman features in their everyday life (such as the consumption of oysters, but also iconic representation clashing with the traditional Druidic aniconism) and to see Rome as a valuable trade and political partner (several Celtica's peoples based their coinage on Roman denarius). Gaul underwent important and quick transformations in the IInd to Ist centuries BCE, many of them probably related to Roman influence, either directly (Rome putting an end to Arvern kingship, and reinforcing Aedun position as the primate people in Gaul, something akin to high-kingship), either indirectly (Roman influence, possibly along with Massaliote, on the constitution of Gaulish "senates; pro and anti Roman parties in Gaulish polities, etc.)

Among other reasons, this is why the notion of "Gallo-Roman" civilization, as if Roman Gaul was a mixed culture born out of roughly equal Gaulish and Roman features, is nowadays importantly criticized in French academia : Roman Gaul was culturally, for all intent and purposes, Roman. Of course, not a stereotyped Roman culture, and with a Gaulish substrate leading to a significant creolization. But this provincial popular culture was largely Roman; and Gaul's elites entirely participating to Roman world since the late Ist century CE, and even more so in Late Antiquity.

Simply said, there was no resurgence because there was nothing to resurge : Gaulish art was gone, Gaulish language was at best on its deathbed, Gaulish spirituality disappeared, Gaulish institutions were history, long before Imperial authority kicked the bucket.

When Clovis, a Frankish petty-king and Roman general, took over most of Gaul, what not just existed but largely dominated was a Roman provincial culture, essentially shared by Franks themselves on the main lines, with only a limited legacy from pre-Roman Gaul.

Most of the former Celtic territories would not experience this resurgence following the fall of Rome, as it would entirely depend on the Germannic invasions.

One of the major causes of the decline of the Roman Empire in the west was the massive migration of Germannic tribes who were themselves being pushed out of their homeland by the invasions of Attila the Hun. By the 5th Century, the Iberian Peninsula was largely under the control of the Visigoths and the Suebo, both Germannic tribes.

Much of what was once Gaul would become Frankia, which is another Germannic tribe that once fought for Rome, but carved out their own kingdom as the empire reached its twilight. There were several other tribes vying for power in this region, most were Germans who had migrated, with a few Celtic tribes trying but failing to reassert any real claim to ancient territories.

Britain is the only place that experienced a resurgence in Celtic tribal control following the withdrawal of Rome in the 5th Century. In what is called Sub Roman Britain, various British (Celtic) tribes, as well as the Picts in the North, and the Welsh (also Celts) would vie for dominance. During this time, the Irish raids on Britain intensified, culminating in the establishment of the Dal Raita kingdom, otherwise known as the Scotti. The Scotti and the Picti would combine crowns in the 9th Century. Britain would of course famously also succumb, at least in part, to the Saxon (another German tribe) invasion, cutting any sort of renewed Celtic autonomy short.

There was also British settlement in present day Brittany, which has retained some semblance of Celtic identity even until today. In addition, some migrating Britons settled in the North of Spain, but I do not know the extent of their survival beyond the Visogothic invasion.

So to make a long story short, after Rome fell those Celtic areas that still existed were overrun by the invading Germans either immediately or within the next century, and so any autonomy or resurgence they would have enjoyed was short lived.