That's not the right way to approach the de Bello Gallico and it's not really the right way to approach the de Bello Civili either. For one thing, they're not really propaganda as we would understand it, and they're not intended to serve the same purpose. Both works are intended to present rhetorical arguments intended to persuade their readers through rhetoric as to the validity of a certain position. Caesar by and large doesn't play particularly fast and loose with the facts at all (he rarely needed to, for one thing), and the political value of his works largely rests in his rhetorical arguments for why events occurred or why particular decisions were made. Even then he doesn't really lie about things, although he'll emphasize or downplay to a certain extent--the degree to which Caesar's work is or isn't reliable I discuss to some extent here. In many ways Caesar is one of our most reliable historical sources from antiquity, period--Tiako points out his two most important points of rhetorical fudging in the de Bello Gallico, the British and German expeditions, but as you see from his description, and as is obvious from Caesar's writing, he doesn't really lie about anything in those passages, he just doesn't present it in such a way as to be completely forthright with his reasons for the expeditions and what exactly people were thinking and doing. He's just sort of cagey about it, he doesn't really express many falsehoods in regards to his descriptions of those events--it's mostly rhetoric, not the changing or invention of actual events.

So there's not really anything to prove false. And indeed, Plutarch, Appian, Cassius Dio, Suetonius, and Cicero all pretty much support the events that Caesar describes. By and large Caesar's really quite a reliable source, one of our best (and easily the single best source for descriptions of battles, not even Arrian comes close). This is to be expected if, as is frequently conjectured, the texts represent edited versions of his dispatches (what Cicero calls the litteras ad senatum that a promagistrate should send back to report his activities)--the senate to which such dispatches were read would've been perfectly capable of fact-checking a promagistrate's story