Why does the letter ‘o’ appear in the word ‘people’?

I consulted Jesse Sheidlower, an editor-at-large for the Oxford English Dictionary. He said that my characterization of the Middle English form as having been peple or peeple was incorrect, and that “Middle English had a tremendous number of spellings”, the ‘eo’ form among them. So my idea that the ‘o’ was dropped and later revived is certainly wrong. Rather, the many other forms died out, leaving only the ‘eo’ form that we still have. Mr. Sheidlower says “it's not clear why the 'eo' form became the standard one”. It seems likely that there is no definitive answer to the question of why ‘people’ now has an ‘o’.

People: late 13c., "humans, persons in general," from Anglo-French people, Old French peupel "people, population, crowd; mankind, humanity," from Latin populus "a people, nation; body of citizens; a multitude, crowd, throng," of unknown origin, possibly from Etruscan. The Latin word also is the source of Spanish pueblo, Italian popolo. In English, it displaced native folk.

Source: etymonline

Looks like the Latin influence is responsible for the "o"

Latin populus meaning folk. populus Romanus - the Roman folk or all the Romans or all Roman people.The Latin o changed in French to a vowel between o and e (le peuple) and in English the o became /i:/. Instead of writing ee one chose to write eo to show the connection with Latin populus.In German there is still the word der Pöbel, meaning people of the lowest social level.