The answer is COIFFEUR or SALON DE COIFFURE. Actually, coiffeur means hairdresser, but in French we actuallu say we're going to the hairdresser instead of I'm going to to the hair salon (je vais chez le coiffeur). Voila! (NB: Coiffure means hairstyle)
Portland Beauty Supply
The real answer is Salon Coiffure.
The French translation for the words Hair Saloon are
Salon de cheveux