Like explained elsewhere, the idea of the stroll, roaming, dilly-dally up to the case of the mesmerized bystander and such i.e. flâner and others are useful. At the same time, it's more focused on the behavior of the watcher as opposed to what they are doing, which is really what we have here: "watching people, to watch people" but coined as an activity, not unlike bird-watching (uses Greek-based ornithologie in French), whale watching etc.. The verbs regarder, observer and étudier will work with gens, autres, homme, femme, nature, réalité, vie, amongst others.
"Observer" often has this idea of some control over the situation; when a person is "placed under surveillance" at the hospital i.e. is being monitored, the person is "en observation" (mind the "observation des êtres vivants", generally medical in a similar fashion; and "observance" related ideas.). But the verb and the word allow for using your senses such as eyesight and observing directly and empirically, paying attention to what you look at, as opposed to the "experimentation" setup/abstractions. "Regarder" allows for many variations with the manner and intensity of the looking, including regarder "d'un oeil distrait, du coin de l'oeil, au loin, de près, en dessous". And "étudier" some such things as the "manière d'être ou d'agir de quelqu'un" is possible in context; but using "human beings/people" without context and this verb eventually leads to the definitions of fields such as "anthropologie, sociologie, psychologie" etc. See also surveiller, guetter, épier, all more secretive and often implying further motivations, so less applicable here.
— Quelle est ton activité préférée ?
— Regarder les gens; observer
les gens/l'être ou les êtres humain(s). Je m'en vais flâner au parc où j'aime bien aller m'asseoir sur un banc avec mon journal et regarder/observer les gens/les passants; c'est ce en quoi consiste le « people-watching ». J'aime prendre le temps d'observer ce que croise mon regard et ce qui m'entoure, avoir l’œil qui regarde bien.
In so many words something close to the literal translation, using the infinitive instead of the continuous, works; add "j'aime/je vais" before, and a complement of location after, to restrict the scope to some activity and place so as to provide context.