Search derives from the Old French cerchier (compare to the Modern French chercher). This derives from Latin verb, circo meaning ‘I wander’, or ‘I go about’. Circo is formed from the Latin noun circus meaning circle and the suffix -o, which forms first conjugation verbs out of nouns, such as donum – dono, or ‘gift’ to ‘give’.
Circus in Latin does mean circle, but also the stadium where Chariot races were held, such as the Circus Maximus in Rome. It derives from the Greek κίρκος (kírkos) meaning circle. The etymology of the Greek is uncertain, but it is likely Indo-European, given that there is a similar word in Sanskrit चक्र (cakrá), which is descended from the Proto-Indo-European *kʷékʷlos, which is also the origin of the Slavic коло (kolo). We know that Indo-Europeans had invented the wheel, as architectural finds have included bronze examples.
Related to search in English is research, where the re- prefix intensifies the meaning, and dates to Old French and recerchier,
To seek is in fact not related to search. Seek has Germanic, not Romance, origins. The Old English secan was influenced by the Norse soekja, both of which ultimately derive from *sokjan in Proto-Germanic, which is descended from a Proto-Indo-European * *seh₂g- meaning ‘to track’ or ‘seek out’. This is related to the German suchen. There is in fact a Latin word descended from this PIE root, sagio – meaning to perceive quickly or acutely with the senses or intellect.