Eating a limb involves grabbing on and chowing down, it's not exactly a quick thing.
Heck, post-skip Franky's arms are big enough that it'll take a fair number of bites to get through. Let alone General Franky! That'd be a really big meal that'd take some time, time that Franky's not likely to give.
Now that i think about it, i feel like in this kind of fight pre skip franky would fair a better chance because post hasnt shown anything like "franky boxing" just the beam. If anything that would lose it for him.
Anything he can do Preskip he can do better postskip, he did an entire body upgrade using Vegapunks super advanced robotics.
He also added things like missiles with gigantic explosions.
Coud de vent was able to blow through several feet of solid metal preskip and we know his power supply has more than tripled since then, a full power burst should finish off Gajeel.
i always thought franky would win but as a brawling perspective, he is not what he used to be and i really dislike that, whatever happend to his being based off of popeye?