I'm not so sure. I just skimmed over the transcript, and yeah, Paris is the POV character in the early part of the episode and then has his moment of redemption at the end, but in between he doesn't have that much dialogue or action. He has about half as many lines as Janeway, though more than anyone else. And he's more reactive than proactive. Janeway talks him into joining the mission. Harry's the one who catalyzes their friendship by reaching out to him, making him want to respond in kind. And Chakotay basically guilts Tom into wanting to make amends for betraying him.
Technically (as David Mack explained it to me once), the strict definition of "protagonist" is the character whose actions catalyze the story. The protagonist is the one whose efforts to achieve something set the story in motion, and the antagonist is the one who tries to prevent them from achieving it. (Which means that often the hero of the story is not the protagonist in the strict sense; for instance, in your typical superhero story, the villain is often the protagonist, the one trying to achieve an act of violence or revenge or conquest, and the hero is the one trying to stop them and is thus technically the antagonist.) So a reactive character like Paris doesn't really qualify. In the case of "Caretaker," I'd say Janeway is the protagonist, because she catalyzes events by pursuing Chakotay's ship, and then by trying to escape the Caretaker, and then by choosing to destroy the Caretaker's array. Though you could say that most of the characters are protagonists of their own subplots, since they're all trying to achieve different things -- Chakotay and Torres want to escape, Paris wants to redeem himself, Kim wants to prove himself, Neelix wants to save Kes, Kes wants to discover the universe.
