The language skills of ropers have varied by edition:
The original roper, in the original Monster Manual, had Exceptional intelligence, but no listed ability to use language.
In second edition’s Monster Manual, the roper is much the same. The Habitat/Society and Ecology sections make no mention of language, and the best we get is “Ropers are not social and do not cooperate with each other.”
The 3.5e roper spoke Terran and Undercommon.
In 4e, those changed to Primordial (which replaced the elemental languages) and Deep Speech (which was said to also be known as Undercommon).
In the preview for 5e, “D&D Next,” that Hoard Of The Dragon Queen was written for, ropers could speak, but they lost that ability by the time 5e was properly published.
It is notable that, prior to 5e, the ropers published by TSR could not speak, but the ropers published by Wizards of the Coast could. For whatever reason, with 5e Wizards decided to go back to TSR’s original.
Anyway, clearly, having a roper who is capable of speech is not exactly unreasonable, and could be done in 5e as a houserule. It would make that encounter in Hoard Of The Dragon Queen run more closely to its intent.
As for which languages, in 5e, Primordial returns (and explicitly has Terran as a “dialect”), as do both Deep Speech and Undercommon, now as separate languages. Deep Speech seems to be used more by the monsters of the deep (e.g. beholders), while Undercommon is more for the more-or-less “civilized” races of the underdark (e.g. drow). Previously, these monsters and races had spoken the same language.
So in 5e, Primordial (with a Terran accent) would definitely apply, and either or both of Deep Speech or Undercommon. Ropers seem more like beholders than drow, to me, so I’d probably go with Deep Speech.