Nope. Here's what etymonline has on the matter:
v.
mid-14c., from Old French refraigner "restrain, repress, keep in check" (12c., Modern French Réfréner), from Latin refrenare "to bridle, hold in with a bit, check, curb, keep down, control," from re- "back" (see re-) + frenare "restrain, furnish with a bridle," from frenum "a bridle." Related: Refrained; refraining.
n.
late 14c., from Old French refrain "chorus" (13c.), alteration of refrait, noun use of past participle of refraindre "repeat," also "break off," from Vulgar Latin *refrangere "break off," alteration of Latin refringere "break up, break open" (see refraction) by influence of frangere "to break." Influenced in French by cognate Provençal refranhar "singing of birds, refrain." The notion is of something that causes a song to "break off" then resume. OED says not common before 19c.