The electronic edition of the American Heritage Dictionary says that efficiency, related to effect, derives "from Old French, from Latin effectus, from past participle of efficere, to accomplish : ex-, ex- + facere, to make; see dhe- in Indo-European roots."
IE dhe- gave at least 100 words to English, including deed, doom, fashion, defeat, feckless, sacrifice, satisfy, face, synthesis, apothecary, boutique, abdomen, benefaction, efficient, vivify, sacrifice, deface, epithet and prosthesis.
