repair (verb)
"to mend, put back in order," mid-14c., from Old French reparer "repair, mend" (12c.), from Latin reparare "restore, put back in order," from re- "again" (see re-) + parare "make ready, prepare" (from PIE root *pere- (1) "to produce, procure").
fix (verb)
about 1370 fixen set (one’s eyes or mind) on something …; probably borrowed from Old French fixer, from fixe, fix fixed, from Latin fixus, past participle of figere to fix, fasten.
About 1500 fasten, setlle, assign; 1663 adjust, arrange, put in order;
American English 1737 mend, repair; 1790 tamper (e.g., with a jury)
Chambers Dictionary of Etymology 1988
For a thought-provoking exploration of many words in the repair realm, see Christine Byl’s “Notes on Repair” in The State of Repair, “Chatter Marks”, edited by Amy Meissner, pp 41 - 46.