CF4 is an important source of fluorine groups in atmospheric pressure plasma jet (APPJ). In order to obtain reactive fluorine species under atmospheric pressure, noble gas (Ar or He) and CF4 are usually mixed and used as the working gas of APPJ. In this paper, the differences in the discharge dynamics on He/CF4 APPJ and Ar/CF4 APPJ are investigated experimentally. Meanwhile, combined with simulation, the effects of downstream targets with different relative permittivity on the radial propagation range of the plasma plume and the distribution of F-containing reactive species are studied. It is discovered that the addition of a small amount of CF4 (20 sccm) will increase the intensity of He/CF4 APPJ due to the contribution of Penning ionization of metastable He with CF4. Differently, the addition of CF4 will continuously lead to a significant decrease in the intensity of Ar/CF4 APPJ. The radial propagation range of He/CF4 APPJ on the target surface decreases with the increase in the relative permittivity of the downstream target. The smaller relative permittivity inhibits the axial propagation speed of APPJ, but it increases the radial propagation range of reactive species. The larger relative permittivity promotes the production of F-containing reactive species and their flux intensity on the target surface.