Collinear laser spectroscopy was performed on the nuclear ground states of the neutron-deficient isotopes (206,205,204)Fr. A new technique was developed to suppress hyperfine pumping in collinear laser spectroscopy of atoms. This involved high-frequency intensity modulation of narrow-linewidth laser light using fast-switching electro-optical modulators. The nuclear ground-state spins of (206,205,204)Fr were determined to be 3, 9/2, and 3, respectively. Both the changes in mean-squared charge radii and nuclear magnetic dipole moments indicate a departure from single-particle estimates.