Caesar in Gaul was almost entirely the creation of Caesar. Roman governors in general acted more or less independently from the Senate simply by virtue of being a long way away. Things in the provinces happened, and the governor was the guy who was in position to deal with whatever the crisis was immediately. The Senate could and did sometimes issue instructions to governors - one such case is Cicero in Cilicia: some local towns had taken loans from Brutus at outrageous interest and appealed to Cicero for relief, which he was inclined to provide. Brutus got the Senate to issue orders for Cicero to enforce the original terms of the loan. Cicero felt compelled to obey the Senate, although he lawyered himself into a less oppressive interest rate anyway. The point being that even when the Senate did take an interest in administration of a province, and Cicero felt compelled to comply to the Senate's order, he still had wiggle-room.

So, in 58 Caesar becomes governor of the Province (the Mediterranean coast of France today), Cisalpine Gaul (northern Italy between the Rubicon and the Alps) and Illyricum (Balkan coast). He gives his reasons, sort of, for how he got involved in Gaul across the Alps in his commentary on his Gallic Wars.

A sort-of-Germanic tribe living around Lake Geneva called the Helvetii were getting pressured by German tribes starting to migrate west, and decided to relocate to Spain. They asked for permission to cross the Province to get there, and Caesar said no. The reason he gives is that the Helvetii were part of the German coalition that nearly crushed Rome in 100ish BCE, so fuck those guys. The Helvetii tried anyway, and Caesar chased them up the Rhone until he wiped them out.[EDIT: and resettled the survivors back near Lake Geneva]

From there, he was invited by a coalition of Gallic tribes having trouble with a German mercenary Ariovistus occupying a lot of land to get rid of the guy, and Caesar agreed. The reason he gives for this is to stop German migration west of the Rhine. Ariovistus had his own Gallic allies, though, so Caesar ended up fighting in Gaul for ten years pacifying the place.

None of this had much to do with the Senate. Some people in Rome were upset by Caesar's actions; Ariovistus was a friend and ally of Rome, and Cato wanted Caesar removed and tried for war crimes, but the Senate never took action on it.

So, Caesar says he's acting out of a policy to stop Germanic migration. Maybe. He also had a lot of debt, and he needed wars to get money to pay that debt, and he needed wars to bolster his reputation as a general for his political life in Rome. How much of his stated reasons are propaganda I suppose is up to the judgment of the reader.