Enter
Middle English: from Old French entrer, from Latin intrare, from intra ‘within’.
wiktionary
From Middle English entren, from Old French entrer, from Latin intrō(“enter”, verb), from intrā(“inside”). Has been spelled as "enter" for several centuries even in the United Kingdom, although British English and the English of many Commonwealth Countries (e.g. Australia, Canada) retain the "re" ending for many words such as centre, fibre, spectre, theatre, calibre, sombre, lustre, and litre.
etymonline
enter (v.)
late 13c. entren, "enter into a place or a situation; join a group or society" (trans.); early 14c., "make one's entrance" (intrans.), from Old French entrer "enter, go in; enter upon, assume; initiate," from Latin intrare "to go into, enter" (source of Spanish entrar, Italian entrare), from intra "within," related to inter (prep., adv.) "among, between," from PIE *enter "between, among," comparative of root *en "in."
Transitive and intransitive in Latin; in French intransitive only. From c. 1300 in English as "join or engage in: (an activity);" late 14c. as "penetrate," also "have sexual intercourse" (with a woman);" also "make an entry in a record or list," also "assume the duties" (of office, etc.). Related: Entered; entering.