This would depend on your setting
Each world has different monsters and different numbers of them. There cannot really be a generic answer to this.
For what it's worth, my bet would be on Undercommon if your world has an Underdark -- it's like a second world below the world.
This is also supported by monster count for the languages - Halfling is listed as a common language, but only 6 monster types speak it, while Abyssal is listed as an uncommon language, but 134 monster types speak it. So counting by monster type, even by the game rules, does not determine how common a language is.
Monster Count: Draconic is the best common choice
I did a little counting: there are 747 monsters that speak common, 238 that speak draconic, 188 that speak sylvan, and 131 that speak undercommon. The other common languages are much less represented -- Jotun 90, Elven 57, Dwarven 27, Gnome 19, Goblin 15, Orcish 9, Halfling 6. I then did count how many of those did also speak common, for those that have enough monsters to have a chance to win. Out of curiosity, I also looked at Abyssal, even though that is an uncommon language, and so I would exclude it from running.
Draconic wins. Draconic is so high as many fiends that do not speak Common also speak it, as the language of magic, I guess. Abyssal is closely trailing Undercommon. Dragons proper funnily enough nearly all speak Common.
So, I was ready to bet you 100 Rep it is going to be Undercommon, and I would have bet wrong. Draconic is the best option by absolute count and also by your measure with 101 monsters that speak it, but no common, followed then by Undercommon with 79, as the second best option.