The interaction between19F nuclear spins in Teflon and3He spins on its surface has been studied in magnetic fields up to 6 Tesla. At temperatures below 1 K, a monolayer of3He is sufficient to increase the NMR relaxation rate of19F more than an order of magnitude over the value with vacuum or with a coverage of pure4He. With a DLX 6000 substrate, the coupling between the two nuclear species weakens towards 6 T. With an Aldrich substrate, the coupling is still active, but it was not observed that the magnetization of a3He film follows that of19F substrate spins. In monolayer experiments, the field dependence of the fluorine nuclear relaxation time T1F is stronger than a quadratic law above 2.5 T, while with liquid3He this field dependence is reduced to a linear law. Most of the data are discussed in terms of a coupling model, in which the19F-3He nuclear dipolar interaction is modulated by motion of3He atoms. The temperature dependence for T1F points to mechanisms involving vacancies, mass fluctuations or exchange inside the3He surface layer or, in one case, paramagnetic centers, in the3He-19F coupling. The relaxation time of the fluorine dipolar reservoir in the Aldrich substrate is of the order of minutes at 3 K and 2.5 T, even in the presence of3He.