Latin circumspicere meant to look around or act cautiously. Its participle circumspectus is behind the English adjective, through Middle French or Latin. The two components make caution a kind of careful observation.
The source gives alternative borrowing routes rather than proving one exclusive intermediary.
Sources
- Merriam-Webster: circumspect
Circumspectus and circumspicere; alternative Middle French or Latin influence; specere means to look.
- Merriam-Webster: circum-
Circum- means around.
- Online Etymology Dictionary: circum-
Also built on *circum-*: circumference, circuit