"War crimes" is not a concept that would be understood by Roman law. It's an imposition of our modern legal concepts--perhaps not a bad thing, but irrelevant to the discussion of Roman law--to suppose that in a world where mass enslavement and total destruction of settlements were the norm rather than the exception one might be legally prosecuted for some supposedly illegal act on the battlefield. Caesar would have been prosecuted for maiestas, which continues to exist in legal codes as lèse-majesté. Moreover, the burden of the prosecution, according to Suetonius, would probably not rest on Caesar's proconsulship but on the actions of his consulship in 59, by far the better case. Indeed, the movement to prosecute Caesar began well before he entered Gaul, it began even before he had renounced his consulship, while he still had the immunity of consular imperium. If in fact there was a legitimate movement to prosecute Caesar (although Morstein-Marx, in his paper Caesar's Alleged Fear of Prosecution and His "Ratio Absentis" in the Approach to the Civil War, is skeptical that this was not just bluster) for maiestas it was on these grounds, that his consulship had displayed disregard for the law. Any actions in Gaul (mainly, it is argued, leaving his province to cross the Rhine--Gabinius was tried for maiestas for leaving his proconsular province to march into Egypt) would have simply added to the issue, not been the core of it.

I'm not sure the kind of War crimes you are describing are the kind that were leveled against Caesar. Without a specific case to reference, it is possible that these references you are seeing to War crimes are related primarily to his actions while Consul and his defiance of the Senate by crossing the Rubicon into Rome. It's important to remember in the latter case that it was prohibited to move troops into the city except in cases of civil defense or in the event of a Triumph. Unfortunately, the majority of my knowledge on this subject is limited to undergraduate courses on Roman history and I cannot offer the kind of depth usually on display in this Subreddit.

So, what I think is important to your question are two things. First, where have you seen these references to War Crimes by Roman Senators? Are these historical documents or analysis by later historians? Second, do the references to these crimes coincide with the period of time when Caesar was consolidating his power and in conflict with certain sections of the Senate and the Optimates? If so, it is not uncommon for hyperbole to dominate Senatorial "discussion", so these sorts of accusations may have validity but may have been couched in purposefully inflammatory language. If you can provide any sort of document reference or even a time frame of these charges it would assist greatly any expert who would choose to answer your question.