Winter Wolves can translate, if desired
It is indeed possible for a Frost Giant to learn common (example: Harshnag from the Storm King's Thunder adventure)
Also, I've read ToA completely, and found no instance where allowing some giants to know common will break a plot point. Conversely: plot points might be missed if the PCs cannot communicate with the Frost Giants.
The adventure seems to indicate that the Frost Giants will converse with the PCs (with no mention that this will be in a language the PCs are unlikely to understand). Since this is presented as an intentional part of the scenario, it seems like the writers likely intended for at least one of the Giants (especially Drufi, the leader) to speak Common.
Example - ToA p.64 says:
Any character who succeeds on a DC 10 Wisdom (Insight) check quickly recognizes that Drufi's clumsy questions are...
It does not mention needing to know Giant to make this roll. Other statements include
she'll try to ferret out what, if anything, the characters know about... (ToA p.64)
If they admit they've met him but can't (or won't) tell Drufi where he is, she has all the reason she needs to capture the characters and torture the information out of them. (ToA p.64)
... they might help characters who can provide useful information. They immediately attack characters who withhold information ... (ToA p.200)
Regardless, their winter wolves speak both Common and Giant, so they could serve as translators if you decide that none of the Giants speak common (ToA doesn't mention this, so it doesn't seem like the writers intended it, but it's there in the Winter Wolf Stat block...).