An active verb "to find peace in" something

If you're committed to a single word, I would look at the reflexive verbs lull, quiet, or ease. Soothe would work.

The resulting sentence would be something like,

"I lull myself by the river."

"She quiets herself by the river."

But, if you want a single unreflexive verb, I would use unwind or relax (somewhat obvious).

"I unwind by the river."

Consider "I drift away in the trickling of the river"

and "I float away in the trickling of the river."

One obvious one that hasn't been mentioned here is rested.

He rested to the trickling of the brook.

Granted, I find the to to be a little bit awkward, but it helps emphasize that the rest achived was due to the trickling of the water rather than simply resting physically by or physically in the water.

A more metaphorical option would be commune. Generally this means something along the lines of "intimate communication," but since the trickling of the water is a much more nebulous concept it invokes (at least in my mind) some concept of the subject finding peace or attaining some sort of peaceful mental state:

He communed with the steady trickling of the water by the brook.

Hope those help, but I don't think they're any better (or worse) than what's been suggested already.

You could use the verb comfort but would need to add a reflexive, such as himself.

Improve the mood of or restore a sense of well-being to:

While not a single word (and no more succinct than find peace), the phrase take comfort conveys a similar meaning.

Interestingly, the term self-soothe is used to describe the beahvior of infants who can calm themselves without adult intervention.

SUPPLEMENT: You also might consider metaphorical terms such as melted, flowed, merged, floated, glided, dwelt, none of which convey his literal action, but a figurative approach to his feelings.