Silver nanoparticles were produced with AgF as the starting Ag(I) salt, with pectin as the reductant and protecting agent. While the obtained nanoparticles (pAgNP-F) have the same dimensional and physicochemical properties as those already described by us and obtained from AgNO3 and pectin (pAgNP-N), the silver nanoparticles from AgF display an increased antibacterial activity against E. coli PHL628 and Staphylococcus epidermidis RP62A (S. epidermidis RP62A), both as planktonic strains and as their biofilms with respect to pAgNP-N. In particular, a comparison of the antimicrobial and antibiofilm action of pAgNP-F has been carried out with pAgNP-N, pAgNP-N and added NaF, pure AgNO3, pure AgF, AgNO3 and added NaF and pure NaNO3 and NaF salts. By also measuring the concentration of the Ag+ cation released by pAgNP-F and pAgNP-N, we were able to unravel the separate contributions of each potential antibacterial agent, observing an evident synergy between p-AgNP and the F− anion: the F− anion increases the antibacterial power of the p-AgNP solutions even when F− is just 10 µM, a concentration at which F− alone (i.e., as its Na+ salt) is completely ineffective.