Unfortunately this painting as other depictions of Gauls made in the late XIXth century isn't really representating something really close to late indepentent Gaulish equipments or bearings as we understand it today, thanks to decades of archeological discoveries and interpretations.

Still, Lionel Royer didn't just made up what he depicted there : as a realist painter (either for historical scenes like this one, but also depictions of contemporary events as he did for the headpage of Le Petit Journal) he did took inspiration from a nascent archeological discipline and artifacts that fueled the image of a stereotypical, anachronical but not entierely mythical, Gaul : Millet's Vercingetorix, Bartholdi (of Statue of Liberty's fame)'s Vercingetorix, Brennus' figurehead, Fremiet's chef Gaulois, etc. basically a really widespread descriptive set that ended up in advertisment as well as public education.

Accompanied by ancient texts on Gauls (in this case Caesar, whose commentaries inspired this scene, altough badly translated as "[Vercingetorix] surrendered" when "he was surrendered" is likely more accurare) these recents discoveries were the first to provide some realism into the depictions of Gauls. Indeed, Gauls themselves let little descriptions of themselves quite probably due to Druidic influence, either by frowning upon the use of writing to preserve their memory, either by frowning upon iconism in their art (altough it was much less systematical, and contemporary statuary can be found as recently as last year in Brittany, they are either not focusing on equipment or heavily influenced by Roman art)

Let's review Vercingetorix's bearing and equipment in this light.

The hairs are arguably close to Diodoros' depiction (itself possibly taken from Poseidonios), shaved on the front and sides, altough far too unkept for a people that took great care (at least for nobles) to comb, colour and show them as a sign of prestige up to their coins (and generally the whole body, as hinted by this Gaulish toiletry set). We could argue the Gaulish war commander just went trough particularily hard campaigning and besieging but so did conveniently clean-shaven and well-haired Romans.

The mustache, however, is definitely what would bear a savage, a Barbarian imagined by Romans or XIXth century, but most probably not a Gaulish leader and noble. True, Gaulish nobles did have mustaches, but we'd be talking of something closer to a 101 mustache (maybe with a collar beard), maybe thinner, or even no mustache at all! (Vercingetorix' coinage arguably depict a clean-shaven young man, but this could easily be a youthful noble depiction trope borrowing from Appolonic depictions)

(On the topic of Gaulish mustache and beard trimming,this answer might interests you)

As for earrings, altough it gives the Arvern king the cool, if expected outlook, of a barbarian it must be said that while Gauls did adorned their bodies with jewelry, such as torcs, rings and earrings, these tended to be smaller and more sophisticated than something that wouldn't look odd at an illustration of Long John Silver.

The armour is, there, a direct inspiration from the Cuirasse de Marmesse, which is a magnificent artifact...from the Late Bronze Age, around the IXth and VIIIth centuries. It was arguably not that problematic, Gauls being seen as the primordial people of what would become France eventually, but the armour owes a lot to either influence or import from the Villanovan culture and early Etruscan history trough most of Central Europe at this point. The same could be said about the helmets of one of the captive Gauls in the picture

One of the others bears what seems to be the helmet found at Canosa di Puglia, in southern Italy, from the IVth century while Vercingetorix's helmet,thrown at Caesar's feet, is a "Beru' helmet, from the Vth century BCE. That's a testimony to both the search for authenticity from the artist, and of the immense confusion of anything "Celtic" (there gallo-italic) no matter the time period or place : imagine a depiction of the Battle of Verdun with french soldiers with plate armour, morions and horseman's pots to have an idea what we're witnessing there.

Gaulish metalworking and military equipment was, of course, renowed and far more advanced than what these anachronic survivors of a age separated from the events by more than 700 years (!) or, at best, outdated models from only 300 years ago : altough not used by everyone, by far, we should expect of Vercingetorix to bear a Gaulish mail coat, with a woolen cloth similar to this reconstruction. As for the helmet, either a "Alesia" (due to being found in important numbers there), a "Port", "Agen" or maybe something more adorned with a crest and/or feathers, Mediterranean-style, or golden applications.

Vercingetorix's shield seems to be inspired by the Battersea Shield, discovered in the mid XIXth century London, but the artists had the good idea of seemingly using it as an inspiration for a wooden (probably due to the depictions made by Greeks and Romans) shield with golden adornments. It's rather the good time period as well, and if the siege had took place in Britain, all would be fine.

(To be entierely honest, I'm not sure what the round shield is supposed to be, but it certainly looks odd.)