Unfortunately, fragrance free and unscented do not necessarily mean that the product doesn't have a scent nor that it doesn't contain fragrance. There is no legal definition for either term, so they can mean anything from does not contain any added fragrance (the main ingredients may have a scent) to it contains a "masking fragrance" to counteract the scent of the natural ingredients.
I have used the unscented version of Elnet and it does indeed contain fragrance (see ingredient list below). However, it is much fainter than the scent of the regular elnett and dissipates quickly. I have yet to find a hairspray that doesn't have any fragrance at all.
Elnett Unscented ingredients: Alcohol Denat., Hydrofluorocarbon 152a, VA/Vinyl Butyl Benzoate/Crotonates Copolymer, Cyclopentasiloxane, Hydroxycitronellal, Evernia Prunasti (Oakmoss) Extract, Aminomethyl Propanol, Limonene, Linalool, Benzyl Benzoate, Benzyl Alcohol, Isoeugenol, Alpha Isomethyl Ionone, Geraniol, Bis PEG/PPG 14/14 Dimethicone, Citronellol, Butylphenyl Methlyproprional, Citral, Courmarin, Glycerin, Amyl Cinnamal, Fragrance