I didn’t know the English phrase but this might match it:

Ce documentaire¹ m’a pris aux tripes.

¹_{Documentaire is now used as a substantive when referring to a movie so we usually drop film.}

You could use "remuer" or "secouer", that mean the same as "émouvoir", which translate as "move":

Ce documentaire m’a secoué.

Ce documentaire m’a remué.

These can be used along with "tripes" (which means "guts"):

Ça m’a remué les tripes.

You could even use "secoué" on its own:

Après (avoir vu) ce documentaire, j’étais secoué.

These days, "choquer" made its come-back, so the following would be pretty much colloquial as well:

J’étais choqué.
J’ai été choqué par ce documentaire.

In addition, I’d say it would all become much more colloquial with an adverb:

Ça m’a complètement choqué.
Ça m’a carrément secoué.