This is a difficult question to answer for a couple reasons. The first being that our primary sources for continental Celtic behaviour come from a handful of authors that are referred to as the Posidonian tradition, including Athenaeus, Diodorus Siculua, Strabo and Julius Caesar, as well as Posidonius himself.
J. J. Tierney has an excellent article in which he explores how all of these authors relied pretty heavily on the writings of Posidonius, and how, with the exception of Caesar, it's unknown how much (if any at all) contact was sustained between the authors and the Celts. After all, the sheer geographic distance between the writers and the Celts (as well as other barbarians) limited interaction and fostered a situation in which factual information about Celts (and other barbarians) was pretty scarce.
It's also important to recognise that while the authors tend to discuss the exact locations of specific tribes, when they discuss cultural practices they often speak more generally, despite "Celt" being a sort of catch-all term for tribes that were spread throughout Europe and Asia Minor.
But, we do have some similarities that exist in the extant medieval Irish literature that some scholars see as a continuation of a "Celtic" tradition.
For example, Athenaeus tells us (translation not my own, but Philip Freeman's from The Celtic Heroic Age 4th edition:
In the twenty-third book of his Histories, Posidonius says that the Celts sometimes engage in single combat during their feasts. Arming themselves, they engage in mock- fights and sparring sessions with each other sometimes, however, wounds are inflicted and these mock-battles lead to real killing unless the bystanders restrain the combatants
Diodorus Siculus equally comments:
During feasts it is their custom to be provoked by idle comments into heated disputes, followed by challenges and single combat to the death
Scéla mucce meic Dathó (quoted selections here translated by Gantz) tells the tale of a feast that erupts in battle, as the warriors recite their heroic deeds and begin to argue over who is the greatest warrior of them all:
Blows fell upon ears until the heap on the floor reached the centre of the house and the streams of gore reached the entrances. The hosts broke through the doors, then, and a good drinking bout broke out in the courtyard, with everyone striking his neighbour
Also in this tale, we have probably the sickest burn in early Irish myth: when Cet suggests that the greatest warrior, Anlúan isn't here or he would soundly beat Conall Cernach. Conall informs Cet that Anlúan is, in fact, here and proves it by throwing Anlúan's head to his friend.
The practice of head-hunting is told to us by Diodorus Siculus of the continental Celts:
They decapitate their slain enemies and attach the head to their horse's neck
The classical authors also tell us of how, at feast, the champion often gets the best/largest cut of meat and this theme does reoccur: the argument in Scéla mucce meic Dathó begins over a debate of who is the greatest warrior and therefore who gets the best cut of meat. In Fled Bricrenn, we get the same idea as Cú Chulann, having bested the other warriors in combat is given the best cut of meat, referred to as "the champion's portion:"
'Rise Cú Chulaind!' the churl then said. 'Of all the warriors in Ulaid and Ériu, whatever their merit, none is your equal for courage, skill and honour. You are the supreme warrior of Ériu and the champion's portion is yours
Now, while these are similarities, it's hard to connect them directly with continental Celtic traditions, at least in my mind. As mentioned already, we can't know how accurate these depictions are and we can't discount the political bias of Roman authors discussing non-Roman peoples who were occasionally hostile to the Roman empire.
Caesar was looking for a justification for conquest, so he depicts a people who both need to be subdued - due to their barbarian practices and the unstable political system he describes - but who also were ferocious warriors that were something to fear, and therefore needed to be subdued. While Posidonius' writings are lost to us, we know he was a Stoic and his philosophical interest in Stoicism worked its way into his depictions of the Celts: Stoicism holds that the world is continuous with no end, and wise men gifted with divine knowledge lead people to civilisation. This is very similar to the discussion & depictions of the druids, and some scholars (such as Tierney) view this as his own bias shining through.
But even if we assume that the classical authors were writing free of bias and entirely accurately, we still have the difficulty of lumping all these "Celts" together in a single ethnographic unit, and discounting the idea that cultural practices can be dispersed and disseminated through trade and travel.
On top of all that, as discussed best by authors who are more familiar with classical writing than I, such as Fairchild and Rankin, the Posidonian tradition writes similar things about other non-Celtic barbarian tribes: Tacitus has similar comments (and derision) about the tribes of Germania; tribes such as the Getai and Trausi are described as courageous and fearless in battle (as the Celts were;) Alani, Thracians and Scythians are also noted as being head-hunters. Derek Williams in his Romans and Barbarians discusses how there were barbarian clichés that dominated Roman writing and that were reinforced by authors, in attempt to contrast their pleasant, civil society with the barbarians.
So the short version is that it's hard to know, because we don't have too much of a handle on what continental Celtic culture was. The term 'Celtic' is widely applied, but severely underdefined. While we have some depictions of continental Celtic culture, we can't know how accurate it is, and while we have some similarities in early medieval Irish texts, it's difficult to know whether this is a retained cultural practice that survived, or (and what seems most likely to me) that the practices described in the saga material, and as described by the classical authors, were simply common practices in their time period.
Sources:
Cunliffe, Barry. The Ancient Celts. London: Penguin Books, 1999.
Fairchild, Hoxie Neale. The Noble Savage. New York: Columbia University Press, 1928.
Gantz, Jeffrey. Early Irish Myths and Sagas. London: Penguin Books, 1981.
Rankin, H. D. Celts and the Classical World. North Ryde: Croom Helm, 1987.
Tierney, J. J. "The Celtic Ethnography of Posidonius." The Proceedings of the Royal Irish Academy 60 (1960): 189-275.
Williams, Derek. Romans and Barbarians. London: Constable and Company Ltd, 1998.
Also: The Celtic Heroic Age ed. John T. Koch & John Carey (fourth edition) Aberystwyth: Celtic Studies Publications, 2003.