The Bigger Picture- Gaul's Impact on the Classical World
Largely, the Romans had a much greater influence on the Gauls than the Gauls had on the Roman people. The Romanization of Southern Gaul was extensive--and somewhat inevitable--given its proximity to Rome. Campaigns like Caesar’s also led to the Romanization of greater Gaul, but we cannot say the same thing about any extensive Gallicization of the Roman people.
That said, the Gallic culture did exercise some influence over that of the Classical Civilizations, particularly in the area of trade. Gaul supplied Rome with important raw materials--tin, grain, silver, gold, hides--that Rome refined into a variety of products. Additionally, trading cities like Massilia, Aquae Sextiae, and Lugdunum were commercially important, and hubs of cultural sharing. One could simultaneously experience the cultures of Greece, Rome, and Gaul, in some major Mediterranean port cities on the southern coast of modern-day France. Ancient historians (like Livy, Polybius, Cicero) would write about these cities as prime examples of the collision of Classical Civilizations.
Since the Gauls were a warring people, they were also a veritable source for mercenaries. Polybius mentions that the Greeks took advantage of Gallic soldiers, and the Romans heavily used Gallic mercenaries in the Punic Wars against Carthage. The trade of manpower also did not stop at military concerns: Gaul was also a source for slaves.
As they were largely looked upon as a barbaric people by the Romans, and subordinate to themselves, the Gallic laymen appeared very useful to Rome. Gallic tribes would give Rome slaves in return for a variety of goods, namely Roman amphorae filled with wine. This led to an interesting pattern. The Gauls absolutely loved Roman wine, so much so that their own wine culture slowly developed, and thus began the French practice of winemaking (which has obviously developed extraordinarily since then). In this way, a reversal occurred wherein the product the Gauls had originally received from the Romans was now being sent back to Rome and influencing the Roman taste for wine.
Aside from very successful Roman commercial enterprises in Gaul, the Gallic culture did have a noticeably impact of the people of Rome, if only in perception. Despite the fact that there were more similarities between the two cultures than first meets the eye--both were skilled fighting machines, developed some sorts of democratic thinking, had religious systems that resembled each other, and held similar superstitions--the Roman masses chose to concentrate on all that was foreign in Gaul. They were frightened of this “savage” people who fought naked, who committed suicide after defeat (so as not to die at the hands of enemies), and whose deities bore different names than their own. There existed an irony in the fact that the Romans, a civilization founded on military prowess, seemed so much to fear the Gauls for their own warrior ethic.
It seems that the Gauls’ reach extended further than what they could provide materially. Their warlike mentality permeated throughout Classical Antiquity in ways that the goods they provided could not. We cannot say that the Gallic culture ever dominated Roman life, but its influence was not negligible either.

Below is a 3rd century bronze sculpture of a Gallic warrior. The muscular, sculpted body is reminiscent of Classical Greek artwork, even though Hellenistic artwork was emerging at this time.