The Bichon Frise (from French: bichon à poil frisé), formally known as the Bichon Tenerife, Teneride dog or Canary Island lap dog, is a small breed of the bichon type. The striking powder-puff appearance of the Bichon derives from a double coat, with a soft dense undercoat and coarser, curly outercoat, causing the coat to stand off the body and even spring back when patted. A Bunch Of Bichon Frises Doormat. This is a merry, agile breed with an effortless and efficient gait. The Bichon’s looks and fitness make this sturdy little dog a popular family addition. The soft, inquisitive expression enables this breed to worm its way into many hearts and laps.