According to Wikipedia’s summary of the episode:
“Janeway learns that the Briori visited Earth in 1937 and abducted some 300 humans…”
It seems to me that if the Prime Directive was violated it was in the context of the initial abduction in 1937. But the Prime Directive wasn’t violated because there wasn’t even a “Prime Directive” in 1937 to be violated; let alone by an alien species (Briori) with the intent of enslaving 300 captive humans.
Therefore, Janeway did nothing wrong because these humans were “alien” only under duress.
FWIW, a similar conundrum was addressed in the Star Trek: The Next Generation episode, “The Neutral Zone” (S01E26) when the Enterprise came across three surviving humans, out of a total of five, that had been cryogenically frozen in the late 20th century on Earth. They were forced to revive them due the the fact that cryogenic chambers they were traveling them were falling apart. And they were frozen but dead anyway? The issue of the “Prime Directive” wasn’t broached under such unusual circumstances.
Update: Adding actual details from the Prime Directive.
Since I have dug up the actual text of the Prime Directive, I am adding a breakdown of this scenario in this context.
Within the two sections of Prime Directive, the first section doesn’t apply to folks kidnapped in 1937 except for the last section:
d) The exception to this is if said society has already been exposed to the concepts listed herein. However, in that instance, section 2 applies.
One can safely assume that they have “…already been exposed to the concepts listed herein.” when they were kidnapped in 1937 by the Briori.
Thus section 2 applies in a case like this:
a) If engaged with diplomatic relations with said culture, will stay within the confines of said culture’s restrictions.
b) No interference with the social development of said planet.
In the case of point “a”, the Voyager crew did indeed stay with in the confines of the culture’s traditions. And in the case of point “b” the Voyager crew did not interfere in any way with the social development of said planet.
So again, Janeway and crew did the best they could be expected to do when interacting with a society that was derived from humans kidnapped in 1937.