As for his drinking, he had in that neither end nor rule.
As seen throughout the text, insatiability seems to be a theme. Gargantua is a giant and I would say that this would lend itself to Rabelais' humanist approach as man being the center of the experience. There are many instances of the constant cycle of eating and drinking, as well as other bodily functions, which demonstrates that "the body is not in stasis, but in a constant state of flux" (Bromilow 28). Hence the body's insatiability and the line highlighted as drinking had "neither end nor rule."
Bromilow, P. “Inside out: Female bodies in Rabelais.” Forum for Modern Language Studies, vol. 44, no. 1, 1 Jan. 2008, pp. 27–39, https://doi.org/10.1093/fmls/cqm120.