Here's what rhymes with archaique.
                        
                        
                    
                                kike  like  bike  hike  pike  dike  dyke  mike  myc  psych  tike  tyke  alike  unlike  spike  shrike  trike  strike  lookalike  unalike  dislike  ladylike  manlike  jellylike  berrylike  motorbike  unladylike  womanlike  workmanlike  businesslike  sportsmanlike  statesmanlike  unsportsmanlike